A big skillet should be heated at medium-high heat. After giving it a quick nonstick spray, add the chopped garlic, thyme, pepper, and squash and zucchini slices. a tiny dash of pepper and salt as well. Use a pinch of salt and pepper here; the remainder of the ingredients are added to the egg mixture. Cook, stirring regularly, until vegetables are soft, about 7 to 9 minutes. Transfer to a basin and set aside to cool while you make the egg mixture.
Turn the oven on to 350°F, or 177°C. Apply nonstick cooking spray to a square pan or 9-inch pie plate. Put aside.
Whisk the eggs, egg whites, milk, salt, and pepper in a big bowl until well blended. Put vegetables in the preheated pan. After adding the shredded cheese, cover with the egg mixture. Add some grated Parmesan cheese on top.
Bake until the filling is set and no longer jiggles, about 45 minutes. Before slicing and serving, allow it cool on a wire rack for ten minutes. (Take note that because there are so many vegetables without a crust, it may still have some water on the bottom even after cooking and cooling.)
Leftovers of this quiche are excellent! For up to four days, store tightly covered in the fridge.