Heat the oven to 375°F and grease a 9-by-13-inch dish. Toast the tortillas in a dry skillet for 15 seconds per side until flexible.
Brown the beef and onion and drain. Add garlic, cumin and salt for 30 seconds, then fold in the beans and one can of chiles.
Whisk the green enchilada sauce, sour cream and remaining chiles. Spread 1/2 cup in the dish.
Layer four tortillas, half the beef, one-third sauce and 1 cup cheese; repeat. Finish with tortillas, sauce and remaining cheese.
Cover and bake 25 minutes, uncover and bake 8 to 10 minutes more. Rest 15 minutes.