From the back of a ramshackle food court in Toronto's Kensington Market, using little more than a couple of souped-up hot plates and a bar fridge, Francisco Alejandri served complex tostadas, vibrant salads and sweets that were as sophisticated as the space was crude.

The modest operation, called Agave y Aguacate, was the first solo venture for the Mexican-born chef, who came to Canada to study cooking at the Stratford Chefs School before working in some of Toronto's best kitchens: Chiado, Jamie Kennedy Wine Bar and Scaramouche, among others. His cooking at Agave was a critical success – Anthony Bourdain called it "some of the most amazing Mexican takeout north of the border– any border" – but, ultimately, creating labour-intensive dishes in a cramped food stall proved overwhelming. Alejandri closed shop in the summer of 2012, little more than a year after opening, just as Canada, after decades of ersatz chimichangas and spurious fajita platters, was finally discovering Mexican fare.

Today, hour-long lineups are the norm at places with taco-driven menus such as Grand Electric, Playa Cabana and La Carnita in Toronto. Calgary, on the other hand, has acquired a taste for the self-described "posh Mexican cuisine" of Xocolat, where a veal chop served with lentils and plantain will set you back $36. In the past couple of months, Vancouver has seen the opening of Los Cuervos Taqueria y Cantina and Cuchillo, places where homemade chorizo and salsas laced with the corn fungus huitlacoche are the norm.

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All of this is good news for Canadians with a taste for the long-stewed moles of Oaxaca, the bright ceviches of the Yucatan and the crisp, vivid tacos of Baja. It's also good news for Alejandri, who will be opening a full-service, sitdown version of Agave Y Aguacate on Toronto's Baldwin Street before the end of August.

Alejandri knows he's entering a crowded marketplace and he welcomes the competition. "Canada is finally embracing Mexican food," he says, "and now that there's a demand for it and chefs and restaurateurs are realizing that there's money to be made, everyone's working to get better." This new understanding of the cuisine brings with it a rejection of the tired clichés that have long symbolized what a Mexican restaurant should be. "I don't want any sombreros, chili-pepper lights or bright yellow walls," Alejandri says.

The menu at Agave will be more ambitious – and more regionally specific – than his food-stall offerings. And while the high standard of cooking and attention to detail will remain the same, the chef is aiming for something greater: "My heart tells me there's still room to do much, much better," Alejandri says. "Having a proper kitchen, a more concrete plan and staff will allow me to do [so]. I'm hoping that if I work hard enough I can help put Mexican food where I've always known it could be."

By introducing diners to the regional specialties of Mexico, Alejandri hopes to encourage people to explore the cuisine more deeply, not only at his restaurant but also at home. To that end, he has offered his own recipe for the cemita, a sandwich that originated in the Mexican state of Puebla and has become popular all across Mexico. The word cemita, Alejandri explains, refers to both the type of bread used and the sandwich itself. "The most popular one is made with a beef [cutlet], but I decided to do it with chicken because it's a little bit lighter. The traditional cemitas are made with queso fresco, avocado and chipotles – that's it. Through the years, they have changed, so now the most popular one in Puebla has meat, Oaxaca-style cheese (which isn't easy to find here, but you can use mozzarella), chipotle and lots of avocado." To complete the meal, he has also provided one of his signature recipes, a tomatillo salad along with a sweet, crisp jicama and orange slaw. It's a meal that's best served outdoors before the end of summer, kicked off with a chia-seed margarita. The cocktail makes excellent use of an ingredient once reserved for novelty figurines and offers further proof that Mexico's cuisine is as suited to invention as any other.