Process 1 1/2 cups flour, salt, and sugar in food processor until combined, about 2 one-second pulses.
Add butter and shortening and process until homogeneous dough just starts to collect in uneven clumps, about 15 seconds (dough will resemble cottage cheese curds and there should be no uncoated flour).
Scrape bowl with rubber spatula and redistribute dough evenly around processor blade.
Add remaining 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 two even balls and flatten each into 4-inch disk.
Wrap each in plastic wrap and refrigerate at least 45 minutes or up to 2 days.