Heat the chorizo in a frying pan over medium heat, crumbling it with a spatula into fine pieces.
Once the chorizo is beginning to brown, add the onion and bell peppers. Cook until softened, about 5 minutes. Stir in the garlic.
Arrange ⅓ of the tortilla quarters across the bottom of a 9x13-inch pan.
Spread ½ of the chorizo mixture across the tortillas.
Cover with ½ cup salsa verde.
Sprinkle with ½ cup of each cheese.
Repeat, beginning with the tortillas, then the chorizo mixture, then the salsa verde, then ½ cup of each cheese.
Layer the remaining tortilla quarters across the top.
Beat the eggs in a large bowl, then beat in the milk.
Stir the salt and chiles into the egg mixture.
Pour the egg mixture over the casserole.
Sprinkle with the remaining ½ cup of each cheese.
Cover the dish with foil and bake for 30 minutes, then uncover and bake for another 20, or until the egg is completely set. (A knife inserted into the middle should come out smoothly and cleanly.)
Serve immediately with sour cream and avocado, if desired.