1. Cut asadero cheese into 1/8- to 1/4-inch slices and lay in an overlapping layer to cover bottom and sides of a shallow 1 1/2-quart pan (about 9 by 12 in.).
2. Remove and discard stem, seeds, and veins from chili. Cut chili crosswise into 1/4-inch slices. Scatter chili and onion over cheese.
3. Stack tortillas, cut stack in half, and set halves together on a sheet of heavy foil (about 12 by 24 in.); seal tortillas in foil.
4. Prepare barbecue for direct heat.
If using charcoal briquets, cover firegrate with a single, solid layer of ignited coals; let them burn down to desired heat. Set grill in place and measure heat.
If using a gas barbecue, turn all burners to high and close lid for 10 minutes. Adjust burners to desired heat. Set grill in place and measure heat.
When grill is medium (you can hold your hand at grill level only 4 to 5 seconds), set tortilla packet and pan with cheese on barbecue. Turn packet over often until tortillas are hot in the center, about 5 minutes; wrap in a thick towel and put in a basket. Heat asadero cheese until melted, 10 to 15 minutes; sprinkle with cotija cheese.
5. To eat, spoon cheese mixture onto tortilla pieces and add tomatoes to taste. Wrap tortillas to enclose filling.