Tear tortillas into 1-1/2-inch pieces. Place on an ungreased baking sheet. Bake in a 350 degree F oven for 10 to 12 minutes or until crisp and lightly browned.
Heat oil in a large skillet. Add baked tortilla pieces, beaten eggs, and salt. Cook and stir over medium heat until tortillas are coated and eggs are set. Stir in Chili Colorado or salsa and 1 cup of the cheese. Simmer, uncovered, for 5 minutes.
Transfer to a serving dish. Top with remaining cheese and onion rings. Makes 4 main-dish servings.