Preheat oven to 375°F (190°C). Lightly grease a 2-quart baking dish; set aside. In an extra-large skillet cook onion in hot oil over medium heat about 5 minutes or until tender, stirring occasionally. Add 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 (960 ml) of the Cotija 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.
To assemble, arrange 5 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 5 tortillas, cutting as necessary to fit. Spread with salsa; sprinkle with the remaining 1/4 cup (960 ml) Cotija cheese.
Bake, uncovered, for 30 to 40 minutes or until mixture is set. Let stand for 10 minutes before serving.