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Make the crust: In a food processor, briefly pulse together flour and salt. Add butter and pulse until mixture forms chickpea-size pieces (6 to 8 1-second pulses). Add ice water 1 tablespoon at a time and pulse until mixture is just moist enough to hold together. Form dough into a large ball. Wrap with plastic and flatten into a disk. Refrigerate at least 1 hour.
Using a lightly floured rolling pin, gently roll out dough to an 11-x-15-inch rectangle, dusting with flour if dough is sticking. Fold dough in half and transfer to a 9-x-13-inch baking dish. Carefully press crust into the bottom of the pan and completely up the edges so it’s flush with the top of the pan (you don’t need to crimp the dough). Return crust to refrigerator while you prepare the filling and crumble topping.
Make the filling: In a large bowl, toss together peaches, sugar, tapioca, lemon zest and juice, nutmeg, vanilla and salt. Let stand 20 to 30 minutes. Taste and add a little more sugar if needed.
Meanwhile, heat oven to 425 degrees. Place a large rimmed baking sheet on the oven floor to preheat. Arrange one oven rack on the lowest position and a second rack in the center position.
Make the crumble topping: Whisk together flour, sugar, cinnamon, ginger and salt. Mix in butter with your fingertips until mixture is uniformly moist and comes together in large clumps.
Assemble the pie: Spoon filling into crust and top with crumble. Move baking sheet to the lowest rack and place pie on baking sheet. Bake 15 minutes. Reduce oven temperature to 375 degrees. Move baking sheet with pie to the center rack. Continue baking until pie is golden brown and filling is bubbling, about 1 hour. Transfer to a wire rack to cool completely before slicing.