Spray 8-inch square (2-quart) glass baking dish with nonstick cooking spray. Place 4 of the tortillas in bottom of sprayed baking dish, overlapping as necessary, about 1/2 to 1 inch up sides. Cut remaining tortilla in half; cut into 1/2-inch-wide strips.
Sprinkle 1/2 cup of the cheese over tortillas in baking dish. Top with chorizo, chiles and 1/2 cup cheese. Arrange tortilla strips over cheese.
In medium bowl, combine eggs, milk, oregano and ground red pepper; beat well. Pour over mixture in baking dish. Sprinkle with remaining 1/2 cup cheese; press lightly into egg mixture. Cover with foil. Refrigerate at least 8 hours or overnight.
Heat oven to 350°F. Bake covered casserole for 30 minutes. Uncover; bake an additional 15 to 20 minutes or until knife inserted in center comes out clean. Let stand 5 minutes before serving. Cut into squares. Serve with salsa.