First, make the crust. This is easiest with a stand mixer, but you can also use a pastry cutter to cut the cold butter into the flour. When the flour and butter mixture looks like little sandy pebbles, you're ready to add some ice water - you might need more than 2 tablespoons, but mixing in the water should bring it all together into a dough. Wrap the dough in plastic wrap and put it in the fridge for a couple of hours.
Take the dough out of the fridge and let it stand about 20 minutes to soften up.
Put some flour down on your work surface, and use a rolling pin to roll out the dough into a circle.
Spray a 9" pie plate with nonstick, and carefully drape the rolled-out dough over the plate. You can neaten up the edges and it isn't a big deal if there are rips and tears -- just pull some overhanging bits of dough off and use them to patch the holes.
Put a piece of parchment paper over the crust, inside the pie plate, and fill it with pie weights (or, I like the use uncooked dry beans) and blind-bake the crust for 15 minutes at 350 °F
Meanwhile, cut up all the vegetables however you like them.
Spray a skillet with nonstick and cook the summer squash over medium-high heat to get rid of some of the liquid inside the squash.
Once the pie crust is done blind-baking, remove the pie weights (or dry beans) and parchment paper, and set it aside while you work on the vegetables.
Arrange the mozzarella cheese and vegetables in the partially-baked pie crust.
Whisk together the half and half, the egg, egg whites, pepper and garlic in a mixing bowl. Pour the mixture evenly over the cheese and vegetables.
Sprinkle the grated parmesan cheese over the top
Bake at for about 40 to 45 minutes, or until a knife inserted into the center of the quiche comes out clean
Transfer the quiche to a cooling rack and let cool for 15 minutes before cutting into 8 slices.