1. FOR THE PIE DOUGH: Process 1? cups flour, salt, and sugar in food processor until combined, about two 1-second pulses. Add butter and shortening; 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 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.

2. 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 4-inch disk. Cover each with plastic wrap and refrigerate at least 45 minutes or up to 2 days.

3. Remove 1 disk dough from refrigerator and roll out on generously floured (up to ? 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. 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.

4. FOR THE FILLING: Adjust oven rack to lowest position, place baking sheet on oven rack, and heat oven to 400 degrees. Process plums and 1 cup halved cherries in food processor until smooth, about 1 minute, scraping down sides of bowl as necessary. 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.

5. 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 ? cup) to 11-inch circle about 1/8 inch thick. Roll dough loosely around rolling pin and unroll over pie, leaving at least ?-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.

6. Place pie on preheated baking sheet and bake 30 minutes. Reduce oven temperature to 350 degrees and continue to bake until juices bubble around the edges and crust is deep golden brown, 30 to 40 minutes longer.

7. 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.