Preheat oven to 375 degrees F. Lightly grease a 2-quart baking dish; set aside. In a 12-inch skillet, cook onion in hot oil over medium heat about 5 minutes or until tender. Stir in garlic. Cook and stir for 30 seconds. Add mushrooms, squash, sweet pepper, and corn. Cook and stir for 5 to 7 minutes or until mushrooms are tender and squash is crisp-tender. Stir in spinach. Cook and stir just until spinach starts to wilt. Set aside.
In a food processor or blender, combine eggs, cottage cheese, and 1 1/4 cups of the Cojita cheese. Cover and process or blend until well mixed. Add cilantro. Cover and process or blend with several on/off pulses until cilantro is chopped.
Arrange five of the tortillas in the bottom of the prepared baking dish, cutting as necessary to fit. Spread with cheese mixture and vegetable mixture. Top with the remaining tortillas, cutting as necessary to fit. Spread with salsa. Sprinkle with the remaining 1/4 cup Cojita cheese.
Bake, uncovered, for 30 to 40 minutes or until mixture is set. Let stand for 10 minutes before serving.