Heat oven to 350°F; spray a 9x13-inch dish.
Cook chorizo in a large skillet over medium 7-8 minutes, breaking up, until browned; add onion and pepper and cook 5 minutes until softened. Drain excess grease.
Whisk eggs, milk, chiles, cumin, chili powder, and salt in a large bowl.
Layer bread, chorizo mixture, and 2 cups cheese in dish.
Pour eggs evenly over filling; press gently to soak bread and top with remaining 1 cup cheese.
Bake 45-50 minutes until eggs set and top is golden; rest 10 minutes.
Serve with preferred toppings. To freeze, cool completely, portion, wrap tightly in foil, and freeze in bags up to 3 months. Reheat foil-wrapped at 350°F for 20-25 minutes.