Put the butter into the freezer for 10 minutes. In a large bowl, combine the flour, ¼ teaspoon salt, and the baking powder. Grate the butter into the bowl using a hand-held grater. Stir to combine, then add the ice water 1 tablespoon at a time and incorporate before adding more. When the dough is combined, roll it into a ball and flatten it into a disc. Then place it in the freezer for 15 minutes.
Flour a work surface and place the dough on top. Add some flour to the top of the dough and to a rolling pin. Roll out the dough into a 12-inch circle. Now transfer the dough to a 9-inch pie plate.
Crimp the corners by pushing in a finger and cupping it with the other hand around the perimeter of the dough or press a fork around the edges. Poke the sides and bottom of the crust with a fork to prevent the dough from puffing out. Put the pie crust in the freezer for 15 minutes and preheat the oven to 375 F.
Crumple up some parchment paper and place it in the center of the pie pan. Pour in some dry beans or pie weights. Bake the pie for 15 minutes. Then remove the weights and parchment and bake for 8 more minutes. Remove from oven and reduce heat to 350 F.
Add the oil to a frying pan and bring heat to medium high. Add the onions and cook for 5 minutes, then add the mushrooms, red pepper, and zucchini. Saute for 10 minutes. In a large bowl combine the eggs, milk, cream, cheese, the remaining salt, and pepper. Add the cooked vegetables and stir.
Pour the mixture into the pie crust and place a large piece of foil under the pie plate and bring it up over the crust edges to prevent those from getting too browned. Bake for 50 to 60 minutes or until the center is set and the top is golden brown. Let it cool for one hour before cutting.