First, make the crust.
In a food processor, combine the gluten-free flour blend, baking powder, and salt.
Add the butter and sour cream and pulse to combine. The dough should be crumbly and rough, but it should be one mass.
If it’s having trouble coming together, add ice water by the teaspoon and pulse.
Once it holds together, turn the dough onto a sheet of plastic wrap and press into a disk, closing the wrap around the dough. It will still seem rough. Refrigerate for 30 minutes.
While the crust chills, make the filling.
In a medium sauté pan over medium heat, add the oil and butter. Once melted, add the onion and sauté for a minute, stirring frequently.
Add the mushrooms and broccoli, salt, and pepper and cook until the browned and the pan has very little liquid (about 10 minutes).
Drain any remaining liquid. In a medium bowl, beat the eggs with milk until well-combined. Keep the veggies and eggs separate until you parbake the crust.
After the crust chills for 30 minutes, parbake it.
Heat your oven to 425°F. While it heats, grease your 9” pie plate. Place chilled dough on a lightly floured piece of parchment paper, dust lightly with flour and roll into a 12” round, about 3/8” thick.
Roll the the pie crust loosely onto a rolling pin and then unroll over the prepared pie plate.
Press the pie crust gently into the bottom and up the sides of the plate and trim so that only 1⁄4” excess is hanging over.
Tuck the excess under itself and crimp gently all the way around.
Pierce the bottom for the pie crust with a fork and place in the freezer to chill for ten minutes.
Remove pie plate from freezer and place a large piece of parchment paper in the center of the crust.
Place pie weights or dried beans in a single layer in the center. Bake for 15 minutes at 425.
Remove from oven, remove the weights and peel off the paper. Reduce the oven temp to 350°F.
Assemble and bake the quiche.
Line the bottom of the parbaked crust with half of the cheese, then the vegetables, followed by the remaining cheese. Pour the milk and egg mixture on top.
Bake in the oven for 35 minutes or until mostly set (just a tiny bit of jiggle in the center) and lightly golden brown. Remove to a cooling rack.
The quiche will set up while cooling for 20 minutes. Serve warm.