1) Heat oven to 350ºF.
2) In large skillet, heat 1 inch vegetable oil to 360ºF. over medium-high heat. Fry tortillas, 1 at a time, until golden brown on both sides. Drain on paper towels.
3) Place tortillas on large baking sheet. Sprinkle each with 1/4 cup Cheddar cheese, 2 tablespoons salsa, 1 tablespoon chilies and 1 tablespoon Parmesan cheese. Bake 8 to 10 minutes or until cheese is melted. To eat, break into pieces.