Heat grill to medium (350° to 450°). Mix ground chuck, salt, and pepper in a large bowl until just combined (do not overmix). Divide into 4 portions and form into 1/2-in. patties with a slight depression in the center of each to help them cook evenly. Brush with 1 tsp. oil.
Rub fresh chiles with remaining 1 tsp. oil. Grill over high heat, turning often, until blackened, about 4 minutes. Cover with a towel to steam, about 10 minutes. When cool, rub off skins, then stem, seed, and slice chiles into strips.
Grill burgers until cooked the way you like, about 7 minutes for medium. In last few minutes, lay a cheese slice on each burger and lay split rolls on grill.
Arrange burgers on bottom of buns and top with one-quarter of chiles and Fritos. Mix mayonnaise and barbecue sauce and dollop about 2 tsp. onto each burger. Set tops of rolls in place.
*Canned Hatch green chiles are available in some grocery stores.
Note: Nutritional analysis is per burger.