In a large bowl, whisk together the flour, salt, and sugar until evenly combined.
Scatter the cold butter cubes and shortening pieces over the flour. Using a pastry blender (or two knives, or your fingertips), cut the fats into the flour until you have pea-sized crumbs with a few larger, almond-sized pieces — those visible chunks are what make it flaky.
Drizzle the cold vinegar and 6 tablespoons of the ice water over the mixture. Toss gently with a fork, then squeeze a handful — if it holds together, it is ready. If it crumbles apart, add more ice water 1 tablespoon at a time.
Turn the dough onto a lightly floured surface and divide it in half. Gently pat each half into a 1-inch-thick disk (do not knead), wrap tightly in plastic wrap, and refrigerate at least 30 minutes or up to 2 days.
On a lightly floured surface, roll one chilled disk from the center outward into a 12-inch circle about 1/8 inch thick, turning the dough a quarter turn every few rolls to prevent sticking.
Loosely roll the dough around your rolling pin, then unroll it over a 9-inch pie plate. Ease (do not stretch) it into the corners, leaving a 1-inch overhang. Trim the overhang, then fold the edge under and crimp as desired.
Fill and bake according to your pie recipe, or blind-bake: line with parchment, fill with pie weights, and bake at 425°F for 15 minutes; remove weights and bake 8–10 minutes more until golden.