Process 1 1/2 cups flour, salt, and sugar in a food processor until combined, about two 1-second pulses. Add butter and shortening; process until homogenous dough just starts to collect in uneven clumps, about 15 seconds (dough will resemble cottage cheese curds and there should be no uncoated flour).
Add remaining 1 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. Divide dough into 2 equal balls and flatten each into a 4-inch disk. Cover each with plastic wrap and refrigerate for at least 45 minutes or up to 2 days.
Remove 1 disk of dough from refrigerator and roll out on generously floured (up to ¼ cup) work surface to a 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. Ease dough into plate by gently lifting edge of dough with 1 hand while pressing into plate bottom with other hand. Refrigerate until dough is firm, about 40 minutes.
Adjust oven rack to lowest position, place baking sheet on oven rack, and heat oven to 400°F.