Slice eggplant and squash, salt and lay on paper towels to drain while you prepare the remaining vegetables.
Line 2 baking sheets with foil and spray with olive oil spray.
Slice pepper, onion and mushrooms and lay out on one of the prepared baking sheets. Cut top of garlic head off to expose cloves and place on pan. Drizzle everything with oil and season with salt and pepper.
Pat squash and eggplant dry and arrange on the other baking sheet, drizzle with oil and season with pepper only.
Place pans in a 400 degree oven and cook for 30 minutes. Remove vegetables to colander and let drain. Lightly chop vegetables and place in a mixing bowl. Add diced tomatoes ans squeeze garlic cloves out of papery shell, and discard shell. Mix garlic into vegetables with your fingers, smushing it to combine and mix in.
Pour a little sauce, 1/4 can into bottom of baking dish. Top with a layer of tortillas, tearing to fit, using about 2 1/2 or 3. Top with 1/2 the vegetables and then all of the spinach. Sprinkle with 1/2 of the cheddar cheese. Make another layer of tortillas and drizzle with another 1/4 can sauce. Top with remaining vegetables, final layer of tortillas. and remaining sauce. Lay on white cheese slices and sprinkle with remaining cheddar. Cover and refrigerate for up to 8 hours.
Bake covered at 350 for 30 minutes, then uncover and continue baking for another 30 minutes or until golden and bubbling. Serves 6-8