Cherry Pie

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.
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.
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.
Preheat oven to 425°F with rack in middle and put a large baking sheet on rack.
Finely grind tapioca in grinder.
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.
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.
Roll out remaining dough on a lightly floured surface with a lightly floured rolling pin into a 12-inch round.
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).
Bake pie on preheated baking sheet 30 minutesutes, then cover edge with a pie shield or foil and reduce oven temperature to 375°F. 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.