Preheat oven to 350°F. Spray a 9x13-inch baking dish with cooking spray.
In a large skillet over medium heat, cook chorizo, breaking it up with a spoon, until browned, about 7-8 minutes. Add onion and bell pepper, cooking until softened, about 5 more minutes. Drain excess grease and set aside.
In a large bowl, whisk together eggs, milk, green chiles, cumin, chili powder, and salt.
Layer cubed bread in the bottom of prepared baking dish. Top with chorizo mixture, then sprinkle with 2 cups of cheese.
Pour egg mixture evenly over everything, pressing down gently with a spatula to ensure bread soaks up the liquid. Top with remaining 1 cup of cheese.
Bake for 45-50 minutes until eggs are set and casserole is golden brown on top. Let stand 10 minutes before cutting.
Serve with your favorite toppings. To freeze: cool completely, cut into portions, wrap tightly in foil, then store in freezer bags for up to 3 months. Reheat wrapped in foil at 350°F for 20-25 minutes.