Dump the flour, sugar, and salt in a food processor and process until combined, about 5 seconds. Toss in the shortening, scattering it evenly over the flour mixture, and pulse until the mixture resembles coarse cornmeal, about 10 seconds. Toss in the butter, again scattering it evenly, and pulse until the mixture resembles coarse crumbs, about 10 pulses. Dump into a bowl.
Sprinkle 3 tablespoons ice water over the flour mixture. Reach for a rubber spatula and stir until the dough sticks together when you press it. If the dough doesn't come together, add the remaining 1 tablespoon water. Turn the dough onto a sheet of plastic wrap, form it into a 4-inch disk, wrap it tightly in plastic wrap, and refrigerate for 1 hour. (You can refrigerate the dough for up to 2 days or freeze it for up to 1 month. If frozen, let the dough thaw completely on the counter before rolling it.)
Remove the dough from the fridge and let it warm up and soften slightly, about 10 minutes. On a lightly floured work surface, roll the dough into a 12-inch circle. Loosely roll the dough around your rolling pin so the pin supports the dough, hold the dough over a 9-inch pie plate, and gently unroll the dough onto the plate, letting the excess dough hang over the edge. Ease the dough in place in the pie plate by gently lifting the edge of the dough with one hand while pressing it against the bottom and sides of the pie plate with your other hand.
Trim the overhang to 1/2 inch beyond the edge of the pie plate. Tuck the overhang under itself so that the folded edge is flush with the edge of the pie plate. Crimp the dough evenly around the edge of the pie plate using your fingers. Wrap the dough-lined pie plate loosely in plastic and freeze until dough is firm, about 30 minutes.
Adjust the oven rack to the lower middle position and heat the oven to 375°F (190°C).
Line the chilled pastry in the pie plate with two 12-inch squares of parchment paper or a double layer of aluminum foil, covering the edges to prevent burning. Fill the pie plate with pie weights, dried beans, or uncooked rice. Bake until lightly golden around thee edges, 18 to 25 minutes. Carefully remove the weights and parchment or foil, rotate the pie plate, and continue to bake until the center begins to look opaque and slightly drier, 3 to 6 minutes. Let cool completely, at least 1 hour.