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1
Blend together flour, butter, shortening, and salt in a bowl with your fingertips or a pastry blender (or pulse in a food processor) just until mixture resembles coarse meal with some roughly pea-size butter lumps. Drizzle 5 tablespoons ice water evenly over mixture and gently stir with a fork (or pulse) until incorporated.
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2
Squeeze a small handful of dough: If it doesn't hold together, add more ice water, 1 tablespoon at a time, stirring (or pulsing) until incorporated. Do not overwork, or pastry will be tough.
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3
Turn dough out onto a work surface and divide into 8 portions. With heel of your hand, smear each portion once or twice in a forward motion to help distribute fat. Gather all dough together with pastry scraper. Divide dough with one half slightly larger, then form each piece into a ball and flatten each into a disk. Wrap each disk in plastic wrap and chill until firm, at least 1 hour and up to 2 days.
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4
Preheat oven to 425u00b0F with rack in middle and put a large baking sheet on rack.
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5
Finely grind tapioca in grinder.
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6
Split vanilla bean lengthwise and scrape seeds into a large bowl with a small knife. (If using extract, add with fruit.) Whisk in ground tapioca, cornstarch, cinnamon, salt, and sugar, then add cherries and toss well. Let stand 30 minutes.
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7
Roll out larger piece of dough (keep remaining piece chilled) on a lightly floured surface with a lightly floured rolling pin into a 14-inch round. Fit into a 9-inch pie plate. Trim any excess dough to leave a 1/2-inch overhang. Chill shell while rolling out top crust.
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8
Roll out remaining dough on a lightly floured surface with a lightly floured rolling pin into a 12-inch round.
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9
Toss cherries well again, then add to shell and cover with top crust. Press edges of crust together, then trim, leaving a 1/2-inch overhang. Fold overhang underneath, then crimp decoratively and brush top crust with milk. Cut out 5 (1- by 1/2-inch) teardrop-shaped steam vents 1 inch from center and sprinkle with sugar (1 tablespoon).
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10
Bake pie on preheated baking sheet 30 minutesutes, then cover edge with a pie shield or foil and reduce oven temperature to 375u00b0F. Continue to bake until crust is deep golden and filling is bubbling in center, 50 minutes to 1 hour more. Transfer pie to a rack to cool completely, 3 to 4 hours.
