1. Preheat oven to 400ºF. Lightly oil 2 8-inch square baking dishes. Line a rimmed baking sheet with foil.
2. In a bowl, combine corn, beans, tomatoes, zucchini, chilies, 1 cup Cheddar and 1/2 cup Monterey Jack. Season with salt and pepper.
3. Wrap 6 tortillas in damp paper towels; microwave on high for 30 seconds. Divide half of filling among tortillas, roll up tightly and arrange seam-side down in a baking dish. Repeat, using second baking dish.
4. Top each dish with 1/2 cup enchilada sauce. Sprinkle with remaining cheese. Place dishes on baking sheet. Bake, uncovered, until bubbly and browning on edges, about 30 minutes. Let cool for 5 minutes.