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1. Process 3/4 cup flour, salt, and sugar in food processor until combined, about two 1-second pulses. Add butter and shortening and process until dough collects in uneven clumps, about 10 seconds; dough will resemble cottage cheese curds. Add remaining 1/2 cup flour and pulse until mixture is evenly distributed, 4 to 6 quick pulses. Empty mixture into medium bowl.
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2. Sprinkle vodka and water over mixture. Fold, pressing down on dough until dough is slightly tacky and sticks together. Flatten dough into 4-inch disk. Wrap in plastic and refrigerate at least 45 minutes.
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3. Adjust oven rack to lowest position and heat oven to 400. Roll out dough on generously floured work surface to 12-inch circle about 1/8 inch thick. Put dough in pie plate and refrigerate 15 minutes.
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4. 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 edge of dough. Refrigerate about 15 minutes.
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5. Remove pie pan from refrigerator, line crust with foil, and fill with pie weights. Bake on rimmed baking sheet 15 minutes. Remove foil and weights, rotate plate, and bake 5 to 10 additional minutes until crust is golden brown and crisp. Remove pie plate and baking sheet from oven.
