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.

Strain puree through fine-mesh strainer into large bowl, pressing on solids to extract liquid; discard solids. Stir remaining halved cherries, sugar, salt, lemon juice, bourbon (if using), tapioca, and cinnamon (if using) into puree; let stand for 15 minutes.

Transfer cherry mixture, including all juices, to dough-lined plate. Scatter butter pieces over fruit. Roll second disk of dough on generously floured work surface (up to ¼ cup) to 11-inch circle about 1/8 inch thick. Roll dough loosely around rolling pin and unroll over pie, leaving at least ½-inch overhang. Flute edges using thumb and forefinger or press with tines of fork to seal. Brush top and edges with egg mixture. With sharp knife, make 8 evenly spaced 1-inch-long vents in top crust. Freeze pie 20 minutes.

Transfer pie to wire rack; let cool to room temperature so juices have time to thicken, 2 to 3 hours. Cut into wedges and serve.