For mom's flaky pie dough: Combine the flour, butter, sugar and salt in a food processor and pulse until the chunks are pea-sized. Add the ice water 1 tablespoon at a time and pulse until the dough just begins to clump together against the walls of the processor.
Dump the dough out onto a work surface and press together to make a cohesive ball, kneading once or twice if it is falling apart. Divide the dough in half, wrap 1 portion in plastic wrap and refrigerate for 1 hour before rolling out. (This recipe makes a double portion of dough; if you are only using 1 portion, wrap the other half in 2 layers of plastic wrap, place in a resealable plastic bag and freeze for another use.)
Preheat the oven to 350 degrees F.
On a well-floured surface and using a well-floured rolling pin, roll out the pie dough into a 9- to 10-inch round. Lightly flour the pin as needed to prevent sticking; if the dough tends to stay sticky while rolling, refrigerate it until firm and begin again. Use a large flat spatula or bench scraper to transfer the dough to a 9-inch pie plate and press into shape using a fork.
Place a sheet of parchment paper or foil into the pie shell and fill with pie weights, uncooked rice or dried beans. Bake until the edges are lightly golden, about 25 minutes. Remove the pie crust but keep the oven on.
For the quiche: While the crust is baking, heat the oil in a medium skillet over medium-low heat. Add the mushrooms and cook until well browned and cooked through, stirring occasionally, 10 minutes. Then add in the mixed veggies to cook out any excess water and wilt the spinach leaves. Remove from the heat.
In a large bowl, combine the eggs, cream, parsley, thyme, nutmeg, salt and pepper in a large bowl and lightly whisk. Sprinkle half of the Gruyere, Cheddar and Parmigiano-Reggiano on the crust, followed by the veggie mixture and then the remaining cheese. Pour the egg mixture over the top and bake until set, about 35 minutes.
Cool for 15 minutes, then cut into wedges and serve.
This recipe makes a double portion of dough. If you only need enough dough for a single crust, wrap the extra ball of dough in two layers of plastic wrap, place in a resealable plastic bag and freeze for another use.