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Preheat oven to 425ºF with rack in middle and put a large baking sheet on rack.
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Finely grind tapioca in grinder.
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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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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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Roll out remaining dough on a lightly floured surface with a lightly floured rolling pin into a 12-inch round.
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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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Bake pie on preheated baking sheet 30 minutes, then cover edge with a pie shield or foil and reduce oven temperature to 375ºF. Continue to bake until crust is deep golden and filling is bubbling in center, 50 minutes to 1 hour more.
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Transfer pie to a rack to cool completely, 3 to 4 hours.