Process 3/4 cups flour, salt, and sugar together in food processor until combined, about 2 one-second pulses. Add butter and shortening and process until homogenous dough just starts to collect in uneven clumps, about 10 seconds (dough will resemble cottage cheese curds with some very small pieces of butter remaining, but there should be no uncoated flour). Scrape down sides and bottom of bowl with rubber spatula and redistribute dough evenly around processor blade. Add remaining 1/2 cup flour and pulse until mixture is evenly distributed around bowl and mass of dough has been broken up, 4 to 6 quick pulses. Empty mixture into medium bowl.
Sprinkle vodka and water over mixture. With rubber spatula, use folding motion to mix, pressing down on dough until dough is slightly tacky and sticks together. Flatten dough into 4-inch disk. Wrap in plastic wrap and refrigerate at least 45 minutes or up to 2 days.
Adjust oven rack to lowest position, place rimmed baking sheet on oven rack, and heat oven to 425 degrees. Remove dough from refrigerator and roll out on generously floured (up to 1/4 cup) work surface to 12-inch circle about 1/8 inch thick. Roll dough loosely around rolling pin and unroll into pie plate, leaving at least 1-inch overhang on each side. Working around circumference, ease dough into plate by gently lifting edge of dough with one hand while pressing into plate bottom with other hand. Leave overhanging dough in place; refrigerate until dough is firm, about 30 minutes.
Trim overhang to 1/2 inch beyond lip of pie plate. Fold overhang under itself; folded edge should be flush with edge of pie plate. Flute dough or press the tines of a fork against dough to flatten it against rim of pie plate. Refrigerate dough-lined plate until firm, about 15 minutes.
Remove pie pan from refrigerator, line crust with foil, and fill with pie weights or pennies. Bake for 15 minutes. Remove foil and weights, rotate plate, and bake for 5 to 10 minutes additional minutes until crust is golden brown and crisp.