Preheat oven to 350°F. Coat a 9-by-13-inch baking dish with cooking spray.
Toast tortillas: place one at a time directly on a burner (gas or electric) set at medium heat. Toast, turning frequently with tongs, until golden, 30 to 60 seconds. Cut tortillas into 1-inch-wide strips.
Whisk 2 whole eggs in a large bowl until foamy. Add flour, baking powder and salt; whisk until smooth. Add remaining 2 whole eggs and egg whites and whisk until smooth. Add cottage cheese, Cheddar cheese, chiles and tortilla strips and mix with a rubber spatula. Pour into the prepared baking dish.
Bake the casserole until set in the center and golden on top, 40 to 50 minutes. Let cool for 5 to 10 minutes. Cut into squares. Serve with salsa.