Combine the flour, sugar, salt, and baking powder in the bowl of a food processor fitted with the metal blade. Pulse a few times to combine.
Add the pieces of butter and shortening and pulse until you have coarse crumbs with lots of pea and chickpea size clumps of butter and shortening within.
Take the dough out of the refrigerator (if it was in the fridge for a long time, let it sit on the countertop for 10 to 15 minutes so it's malleable enough to roll). Dust your work surface lightly with flour and place the dough on top. Sprinkle a little flour over the dough. Use your hands to quickly work the dough into a smooth disc. Don't overwork or warm it up too much, just smooth the edges as best you can so it's easier to roll.
Roll the dough, adding more flour as necessary under and on top of the dough so it doesn't stick, into a 13 inch circle. Carefully drape the dough over the rolling pin and transfer it to a 9 inch deep dish pie pan (it should be least 1 1/2 inches deep). Gently fit the dough into the pan, easing it inwards rather than stretching it outwards. Don't worry if it tears, just patch it right back up. Trim the edges to 1/2 inch beyond the lip of the pie pan. Turn the edges under to create a rim on the crust (you can use the scraps to patch in any thin areas) and then press the rim against the lip of the pan, forming it into an even edge as you go. Using your fingers, crimp the rim. Place the crust in the freezer for at least 15 minutes while you heat the oven.
Preheat the oven to 375. Remove the pie crust from the freezer and place on a baking sheet to make it easier to move in and out of the oven. Cover the crust with a piece of parchment paper and fill it about halfway full with dried beans or pie weights. Bake for 20 minutes. Take the crust out of the oven and remove the parchment paper and beans/pie weights and tent the edges with a few strips of foil folded in half lengthwise. This will protect the edges from getting too dark. Bake for another 20 minutes, until the dough is dry and golden. Don't worry if the bottom puffs up and just press it down gently with a flat spatula, such as a pancake turner, taking care not to puncture it. Remove the foil but don't throw it away. You may need it again.
Reduce the oven temperature to 325.
Make the filling by whisking together all of the ingredients in a large bowl. Pour the filling into the pre-baked crust. Bake for 50 to 60 minutes, until the filling is just set. It should look dry around the edges and the center should jiggle just slightly if you nudge the pan. Keep a close eye on the pie as it bakes. If the crust looks like it's browning too quickly, tent the edges again with the foil strips. Cool the pie on a rack and leave it on the baking sheet in room temperature for a few hours. Slice or refrigerate until ready to serve.