Dice the unsalted butter and shortening and place it in the freezer while preparing the flour mixture. In a food processor fitted with a steel blade, pulse flour, salt, and sugar to combine; add the chilled butter and shortening pieces and pulse until the mixture resembles a coarse crumble with only a few larger pieces, about 8 to 12 pulses.
In a small bowl, combine 3 tablespoons of ice water and 1 tablespoon of pure vanilla extract; with the machine running, pour the ice water mixture down the feed tube and pulse the machine until the mixture is evenly moistened and very crumbly; don't let the dough form into a ball in the machine.
Remove the bowl from the machine, remove the blade, turn the dough onto a work surface, and bring the dough together by hand. Use a bench scraper to divide the dough into two equal pieces. Shape into flat disks and wrap in plastic wrap. Refrigerate for at least 30 minutes, preferably overnight. (Note: Dough can be refrigerated for up to 3 days and frozen for up to 1 month, tightly wrapped.)
Lightly dust a work surface and a rolling pin with flour. Place one chilled pie disk on the work surface and let the dough sit on the countertop for 5-10 minutes so that it's malleable enough to roll; lightly dust it with flour and roll the dough by starting at the center and lightly pressing down with the rolling pin to flatten slightly. (Keep the other disk refrigerated until it's time to make the other pie).
Rotate the pie dough and repeat, pressing down, so it's evenly flattened all around, about ⅛-inch thick. Then roll outward to make a circle, rotating the dough a quarter-turn at a time to keep it even. (If the dough is softening too fast, chill in the refrigerator until firm, 2–5 minutes.)
Roll the pie dough until it's about 2–3 inches larger than the pie dish all the way around, overturn the pie dish onto the center of the dough circle, and use a pizza wheel to trim away the rough edges. Save the scraps to make crust cookies, if desired!
Remove the pie dish and place it right-side up on your work surface. Use the light indentation created by the rim as a guide for gently positioning dough into the center of the dish. (If the dough is softening too fast, put it back into the refrigerator until it firms up, 2–5 minutes.)
Fit crust gently into the dish, pressing firmly against the side and bottom, careful not to stretch the dough. Trim away the excess dough, leaving a ½-inch overhang all around. Fold it under; flute or crimp the edge with your fingers (lightly flour your fingers if the dough is sticking).
Alternatively, you can use the tines of a fork to crimp the edges. Next, prick the bottom of the crust all over with a fork to prevent bubbles; this keeps it from puffing as it bakes; repeat the process with the remaining pie crust. Place the crusts in the freezer for at least 15 minutes while you heat the oven to 425 F.
Next, place the unbaked pies on a sheet pan and line the crust with parchment paper. Then fill the paper three-quarters full with pie weight or dried beans and bake the crust for 20 to 25 minutes until the edges start to brown.
Remove the pie weight and parchment paper (If you're using dried beans, save the beans for another time), and bake for another 5 minutes. Then, remove the pie crusts from the oven and set them aside to cool while preparing the pecan filling.