In a medium bowl, combine the eggs, egg whites, 1/4 teaspoon salt, and a few grindings of black pepper and stir in the mozzarella.

Lightly coat a large, oven-safe, nonstick skillet with cooking spray and warm over medium heat. Add the onions and mushrooms and cook, stirring, 5 minutes. Add the zucchini, red peppers, thyme, 1/4 teaspoon salt, and pinch black pepper. Cook the mixture, stirring, 4 minutes.

Pour the egg mixture over the vegetables and cook over medium-high heat for 7 minutes. As the eggs begin to set, run a spatula around the edges and tilt the skillet to allow any uncooked egg to run under the cooked portions. Do not stir. When the eggs are almost set, cover, reduce the heat to medium-low, and cook for 8 to 10 minutes, or until eggs are set.

Preheat the broiler.

Sprinkle Parmesan on top of the eggs. Broil the frittata for 4 minutes or until the Parmesan is lightly browned. Cut the frittata into 6 wedges.