1. Preheat oven to 400 degrees.
2. In a large skillet over medium heat sauté onions and peppers in olive oil until tender. Add garlic and zucchini and sauté for an additional 4 minutes. Add eggplant, salt and pepper to taste and sauté another 10-15 minutes.
3. Remove from heat and stir in tomato puree. Stir in beaten eggs, Parmesan cheese and half of Monterey Jack or mozzarella cheese. Pour in a 9 x 9 glass square baking dish, and top with remaining cheese.
4. Bake for 20-25 minutes. Remove from oven and let rest for 10 minutes before serving.