Quito is a breathtaking city—but not in the usual sense. Sure, the Ecuadorian capital is gilded and gorgeous, a painstakingly preserved jewel box of Baroque excess that was named one of the first UNESCO World Heritage Sites in 1978. But, at 9,350 feet above sea level, the world's second-highest capital (after La Paz, Bolivia) is also a place that literally takes your breath away. Not helping matters are the gasp-inducing natural surroundings that cluster on either side of the Equator: the alpine páramo grasslands, the snowcapped volcanoes, the misty cloud forests, the swarms of buzzing hummingbirds. So inhale deeply, and dig in.

I continue to Humacatama Sombrería, where artisan Luis López shows me how to craft Ecuador's most famous—and misunderstood—export: the misnamed Panama (or toquilla) hat. Teddy Roosevelt was photographed wearing one of these wide-brimmed straw hats while visiting the canal construction site, which boosted their popularity, but make no mistake: These hats are an Ecuadorian creation, with a spot on the UNESCO Intangible Cultural Heritage List to show for it.

Humacatama Sombrería hatmaker Luis López

López strips the fibers of a jipijapa palm frond with his fingernails. The thinner the strands and tighter the weave, the finer the hat. “You don't get any light through the hat," he says in Spanish, holding one of his creations up to the window. “It takes a year to make the finest hats. But we need to start calling them Ecuador hats!" The highest-quality ones, he tells me, can go for $25,000. It should be noted that these popular souvenirs aren't often seen around town. The preferred head covering, especially among the indigenous women selling fruit and textiles on street corners, are felt fedoras, often decorated with a jaunty plume.

Quito's historic center seems delightfully trapped in time, but there's a vibrant modern city beyond the cobblestones. I hop a cab to Quitu Identidad Culinaria, where chef Juan Sebastián Pérez's tasting menu takes me to the far reaches of this biodiverse country: from the Amazon, paiche, a man-size, air-breathing fish, served with hearts of palm and passion-fruit juice; from the coast, cassava with shrimp and sweet crab; from the Andes—or the petting zoo?—a 72-hour sous-vide llama, an indigenous meat source that's not especially common here in the capital. (For the record, it's very lean and lamb-like.) My three dessert courses include, among other flavors, 72-hour cold brew coffee, a 70 percent chocolate terrine, and both a meringue and a carbonated drink made from guayusa, the highly caffeinated leaf of an Amazonian holly tree…

Which means that, despite the long day, I have plenty of energy for a nightcap on the roof of the Hotel Carlota, a sustainably designed property in a 1905 mansion that was the former HQ of Ecuador's conservative party. After a couple of cocktails, however, I don't even need to count llamas before nodding off.

The staircase at the Hotel Carlota

Day 2:

Straddling the Earth, stalking hummingbirds, and sipping cervezas

Ecuador's star attraction is right there in the name. This is the middle of the world, and Quito practically shouts its location from the rooftops. My goal for the morning is the nation's most obligatory tourist stop: the photo op at the Equator, about 15 miles north of the Old Town, where every grinning backpacker must, by law, bestride the narrow yellow line like a selfie-ing Colossus. I've hired a driver for the day, Jairo Lobo, who whisks us out of town, past miles of pastel houses tumbling Tetris-like down hillsides, to the roadside restaurant Rincón Quevedeño #2, where we have tigrillo, a coastal breakfast of mashed green plantains with stewed pork, queso blanco, and a fried egg, along with frothy blackberry juice.

Fully carbo-loaded, I pay the $2 entry fee to the Mitad del Mundo monument, a 98-foot-tall obelisk topped with a globe that looks a bit like the Daily Planet building. The monument was built in 1982 to commemorate an 18th-century French mission to find the true Equator, but it hides a dirty little secret: The honest-to-goodness 0 degrees latitude is 787.4 feet away.

The Mitad del Mundo monument near the Equator

Down the road sits the scrappy Intiñan Solar Museum. I join a tour that's already in progress, as the guide shows off a case holding a 180-year-old shrunken witch doctor's head that looks like a ham hock in a wig. “They stopped the practice around the 1980s and '90s, because it was turning into a mafia," he says. “They used to sell the heads for $80,000. If it was a shaman, you could pay even more." As we shuffle on to the next exhibit, a Chinese priest in a robe and white collar next to me whispers, with concern in his voice, “But why has it gotten so small?"

The museum's centerpiece is, naturally, the centerpiece of the world. Here, on the magnetic Equator, which was calculated by army GPS 17 years ago, reality operates slightly differently. To prove it, the museum has set up a series of experiments that feel like a school science fair but still earn their oohs and aahs. Water pours straight down a drain without spinning! I can't heel-toe walk along the line with my eyes closed without tipping over! I can balance a raw egg on the head of a nail! Whether these demonstrations are real or show—the mythbusting Snopes.com has some strong opinions on the matter—I leave with a smile and a handwritten egg-balancing certificate.

Lunch is 15 minutes away, at Hotel El Cráter, a pumice stone building perched on the lip of the Pululahua volcanic crater, one of only two populated calderas on the planet. I grab a seat by the window and watch fluffy clouds barrel like freight trains through the valley below. We're (very) close to the Equator, but that doesn't mean it feels like the tropics. High up here in the Andes, the food skews hearty. I order locro de papa, an achiote-dyed potato soup served with shredded cheese, hunks of buttery avocado, and maíz tostada—corn kernels that crunch like the ones you find at the bottom of a bag of microwavable popcorn.

"Here, on the magnetic Equator, reality operates slightly differently. I leave with a handwritten egg-balancing certificate."

Past Hotel El Cráter, the road shifts; mist envelops the shoulders as we descend into the Mindo Cloudforest, a high-altitude jungle that attracts whitewater rafters and zipliners. We pull into the Alambi Reserve, a sanctuary for more than a dozen hummingbird species. I grab a seat on the porch and look out on a yard lined with feeders and flowers that—there's only one word for it—swarms with birds. They come in droves, buzzing, dive-bombing, darting, slurping sugar water. I practice my wildcat-stalking skills as I slink like a moving statue to within inches of the feeders to snap photos. Nectar-drunk, the birds barely react.

A hummingbird at the Alambi Reserve

Down a hill, I meet Brian Krohnke, an American expat who runs Cloud Coffees. Here, on five acres of the reserve, he's growing seedlings that will help to reforest this area. “We're one of the highest growers in the world," he says, as he sorts beans drying in the sun. “These come from 1,800 meters." I buy a bag of his shade-grown coffee from a makeshift wooden structure. Krohnke tells me to expect citrus, lilac, and vanilla notes, but the biggest selling point for me is the label: a dreamy-eyed sloth holding a mug of joe.

A pacific oyster with Amazonian jelly at Urko Cocina Local

I get back into town in time for dinner at Urko Cocina Local, in the buzzing La Floresta district. I order a frozen canelazo (of course) and then dig into a tasting menu that sees chef Daniel Maldonado remixing Andean staples. An octopus ceviche dotted with roasted peanuts is followed by lamb croquettes in a naranjilla beer sauce and spoon-tender suckling pig with cheese foam. I finish my meal with an ode to the nation's beloved corn, a deconstructed dessert of corn mousse, corn with cheese, and purple corn biscuits.

Back in the historic center, I seek out a different staple grain at Santa Rosa Cerveza Artesanal, one of a growing roster of craft breweries in the city. I order a peach sour beer and grab a seat in the Scandi-chic taproom, by a window that looks out on the illuminated Baroque church of St. Augustine. I'm confident that the patron saint of brewers would have enjoyed this next chapter in Quito's development.

The modern taproom at Santa Rosa Cerveza Artesanal

Day 3:

Scaling a volcano and playing cowboy for a day

“You feel OK?" I'm in the TelefériQo, a glass gondola that's rapidly ascending the side of the Pichincha volcano. It's only natural that my tour guide for the day, Gaby Cifuentes, is checking on me. Within 18 minutes we'll be gliding up, over eucalyptus forests and cattle pastures, to a preposterous 12,943 feet. This is prime altitude sickness territory, but I assure her that, save for a few ear pops and some slightly shallow breathing, I will survive.

Colorful houses built into the hillsides of Quito's volcanic valley

We hop out at the summit, where we can see our breath in the cold morning air. From here, we hike, slowly, up a scruffy hillside to 13,287 feet, where we have a clear view of the city's contained sprawl, which snakes for 25 miles through the volcanic valley below. We keep our pace glacial to fight, you know, passing out, as more adventurous types surround us on all sides: above, hikers follow a trail that tops out at 15,406 feet, while below us hang gliders catch the wind.

“We feel OK now, but we have to remember to drink water," says Cifuentes. At the summit café, next to a seemingly empty oxygen bar where you can inhale flavored air, we rehydrate with coca tea and munch on melcochas, a sugarcane candy that's said to help with altitude sickness.

"We drive out of town, past miles of pastel houses tumbling Tetris-like down hillsides."

Now that we've gotten our sea legs—sky legs?—Cifuentes wants to show me an even more impressive landscape. We head south on the Pan-American Highway, which stretches nearly uninterrupted for 19,000 miles from Alaska to Tierra del Fuego. This part, which is perfumed by Tasmanian blue gum eucalyptus trees and skirts seven mountains, is called the Avenue of the Volcanoes. As we continue along, Cifuentes and my trusty driver, Lobo, tell me about their side gigs (her family has been making guitar strings since 1906; he works for a line of infused spirits named, appropriately, Los Volcanes). We pass fields of black-and-white Holsteins. “The beef from here is tough," says Cifuentes. “It's the Andes, so our cows have to be athletic."

We turn off the highway and onto an exceedingly bumpy road—staying upright in the back seat is an intense core workout—which opens up into an alpine tundra grassland, or páramo, where we find the thatch-roofed Hacienda el Porvenir, on the sprawling ranch and eco-resort operated by the tour company Tierra del Volcán. Inside, we warm up with empanadas and mugs of—what else?—canelazos in front of the fireplace. I'm here to hit the trails on horseback. But before I do, I refuel in the hacienda dining room with owner Jorge Pérez.

A mug of canelazo at Hacienda el Porvenir

“This hacienda was bought by my great-great-grandmother," says Pérez. “Porvenir translates to 'what's to come.'" This plot was first settled in the 17th century by Jesuits who raised sheep and llamas. When indigenous people started stealing their livestock, they brought in sleek black fighting bulls from Spain to ward off intruders. “They taught their most trusted employees to ride horses to handle the bulls," says Pérez. Thus, the high-Andean cowboy, or chagra, was born. “They became the first indigenous peoples to be allowed to ride horses in all of the colonies. Being a chagra became a status symbol."

After a lunch of Andean ceviche (marinated lupini beans and hearts of palm) and beef tenderloin with Andean huckleberry sauce and ishpingo (a dried flower that tastes like cinnamon), I'm ready to hit the trails. Laura, a volunteer who moved here from Seattle to escape American politics, looks me over as I head toward the paddock. “We have to get you to look like a chagra," she says. I step into a pair of chaps and slip on a wool poncho that's as heavy as one of those lead vests at the dentist. In place of a cowboy hat, I'm fitted (thankfully) with a helmet.

The thatch-roofed Hacienda el Porvenir

“What's his name?" I ask, stepping up to a criollo horse, a breed known for being compact but strong.
“Piquero," says my guide.
“What's that mean?"
“Booby."
“Booby?"
“Not that kind of booby." (Oh right, I think: the blue-footed kind.)

We trot out into the resort's nearly 2,500 acres of grassland in the shadow of Cotopaxi, a snowcapped active volcano.

As we pass through fields of llamas and fighting bulls, I look down to make sure my striped poncho doesn't have any bright red to antagonize them. Safe. My eyes are peeled for ultra-rare condors, but I keep getting tricked by carunculated caracaras, black birds of prey that, while beautiful, don't rank as high on my birdwatching bucket list. Piquero, unimpressed and docile, keeps stopping to munch the grass, the same scruffy brush that makes up the hacienda roof.

A llama at the Tierra del Volcán resort

Horseback riding sounds like a mosey in the park, but it's surprisingly tiring. (My poor thighs!) Back in Quito by sundown, I've more than earned my dinner at the impossibly lavish La Belle Epoque. This French-Ecuadorian restaurant, dripping with red velvet curtains and towering candelabras, sits on the second floor of the Hotel Plaza Grande, which occupies Pizarro's old digs on the Plaza de la Independencia. While the setting is Continental, the menu offers perfect takes on Andean classics. I order a sangria-like rosero, made with orange-blossom water, pineapple, lemongrass, strawberries, and hominy that's been sliced with a razor blade, Goodfellas-style. After a creamy locro de papa and roast pork with peanut salsa, the lights suddenly go out, and music starts blasting through the dining room.

From the kitchen emerges a cucurucho, a purple-robed figure in the cone-shaped hood that gives him his name (an outfit that would certainly not fly in America) . These penitent sinners usually walk through Quito's Old Town during Holy Week, carrying cripplingly heavy crosses, some whipping their own backs, some bleeding from the barbed wire they've wrapped around their bare chests. This cucurucho, however, is carrying a copper pan, foggy with dry ice, that holds three little scoops of ice cream: blackberry, guanabana, and fig and cheese. Should we repent for the sin of gluttony?

It feels like an oddly blasphemous interlude for a place with this much reverence for history and tradition and faith. But in a city with nearly a half millennium of history under its belt, it's not uncommon to see the old butt up against the new, the sacred against the profane, the Baroque against the bargain basement. I pull out my phone to try to capture the scene, but the lighting is all wrong and the music doesn't translate. This, I realize, is the kind of off-kilter experience you just have to sit back and enjoy, in a place where even the dessert course comes with a little something extra—la yapa.