Lightly grease a 2-quart rectangular or square baking dish; set aside. In a 12-inch 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. Remove from heat.
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 combined. Add cilantro. Cover and process or blend with on/off pulses until cilantro is chopped.
To assemble lasagna, 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 five tortillas, cutting as necessary to fit. Spread salsa over tortillas; sprinkle with the remaining 1/4 cup Cojita cheese. (To serve today, omit Step 4. Continue as directed in Step 5.)
Cover baking dish with plastic wrap. Chill for 2 to 24 hours. To serve, let stand at room temperature for 30 minutes.
Preheat oven to 375 degrees F. Bake, uncovered, for 30 to 40 minutes or until mixture is set. Let stand for 10 minutes before serving.