ONE September afternoon before Mexican Independence Day, Rick Bayless was sampling fare at crowded market stalls in the city of Puebla when he sat down for a meal he would never forget. ''It was the height of the season. The peaches, nectarines, and walnuts were just mature,'' recalls the award-winning chef. ''I ordered a special festival dish and was eating it. I loved the balance of fruit and filling,'' he said of the Chile Stuffed With Minced Pork and Fruit in a Creamy Walnut Puree. The woman working at the grill, delighted by Mr. Bayless's interest, sent her daughter out to buy each of the seasonal ingredients of the dish. Then she enthusiastically showed him every laborious step of concocting the Chiles En Nogada (chiles in nut sauce), considered the region's crowning glory. ''That's what's so special about Mexico - how much life the people have,'' Bayless says. The vignette also hints at what's so special about Bayless - his passion for Mexican culture. Winner of the James Beard Foundation's 1995 Chef of the Year award for his renowned Mexican cooking - Bayless's fascination with Mexico began as a boy growing up in Oklahoma and led to a bachelor's degree in Spanish and Latin American culture. In 1981, Bayless quit doctoral studies in linguistics and made a four-year pilgrimage to Mexico with his wife, Deann. They crisscrossed the country sampling dishes at exotic market stalls, street-side cafes, and tiny snack shops, drinking in the flavor and flair of grassroots Mexican cuisine. ''I spent most of my time tasting to try to figure out what flavors they were going for,'' says Bayless, who grew up working in his family's Oklahoma barbecue restaurant. ''It's like learning a foreign language, you have to get the accent right.'' The fruit of Bayless's southern expedition was an acclaimed cookbook, ''Authentic Mexican: Regional Cooking From the Heart of Mexico'' (1987, William Morrow, 384 pp., $24.95). That same year in Chicago, Bayless opened Frontera Grill, which specializes in Mexico's colorful, varied regional dishes. In 1989, he opened the upscale Topolobampo next door. This month, in celebration of Mexico's Sept. 16 national day and perhaps also of the memorable meal in Puebla, Bayless will offer Chiles en Nogada in both of his restaurants. As he serves a kaleidoscope of regional specialties, Bayless strives to perfect what he believes is the essence of Mexican food: the sauce. The sauce is the critical component, and what is most purely authentic,'' says Bayless, noting that Mexican dishes are named after their sauces. Chiles, the chief ingredient of many sauces, are carefully prepared in the traditional fashion. Whole chile pods are dried and toasted on a grill. Next they are soaked in water and pureed. Finally, the puree is fried in a sizzling hot pan and left to simmer until it forms a thick paste. In the kitchen at Frontera Grill, Bayless offers tastes of a savory green sauce, or mole verde, from central Mexico. Combining green chiles, ground pumpkin seeds, and tomatillos with cilantro seeds, cinnamon, and cloves, it is served over chicken. Another, sweeter, mole colorado blends red chiles with plantains, raisins, and almonds. A gravylike, rich chichilo mole for use with beef mixes red chiles with darkly baked tortillas to create a slightly toasted flavor from the region of Oaxaca, home to Mexico's most complex cuisine. Just across the counter from Bayless in the kitchen, a small Mexican woman tends to another essential ingredient: the tortilla. The woman, Aedilia Neri, methodically pinches pieces of masa, or corn dough, from a bowl. The masa is made each morning from starchy white field corn that is dried, then partly boiled and ground with a stone grinder. (Metal grinders aren't used because they heat up and cook the corn, Bayless explains.) Mrs. Neri flattens the masa in a traditional iron press, then bakes it, flipping it twice so it puffs up on the griddle. She makes as many as 2,500 loaves of the flat breads each day. Once cold, the tortillas are served without being reheated. ''It's the Mexican equivalent of bread fresh from the oven,'' Bayless smiles. Ever the translator, Bayless admits that he still cooks Mexican food ''with an American accent.'' Partly this is an intentional effort to bridge the gap between what most Americans consider Mexican food - spicy burritos and tacos - and the vastly more complex reality. ''If I did a literal 'translation' to a non-Spanish audience, I wouldn't get very far,'' Bayless says. In deference to the meat-centered diets of many Americans, Bayless often serves whole pieces of meat. In Mexico, meats are usually cooked in stews because it is cheaper and masks the poor-er quality of local meat. He also spends ''a lot more time'' garnishing food. Still, these nods to American tastes detract nothing from the overwhelmingly Mexican feel of his restaurants. Primitive paintings, bold masks, and fantastical figures called alebrije - all collected from Mexico by Bayless himself - create a vivid decor. Indeed, Bayless only wishes that his love for Mexican cooking were something Americans felt more strongly for their own culinary culture. In this age of microwaves, fast food, and frozen TV dinners, Bayless laments that children are missing a basic skill and source of sharing. Every child should learn how to bake a birthday cake, Thanksgiving turkey, or to cook another dish that is part of the family's tradition, he says. ''By serving food for someone, you can communicate very strongly in a non-verbal way. You can create a sense of belonging,'' he says. ''One of the ways we build community is by sharing the table together.''