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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. Add ice water, 1 tablespoon at a time, and pulse until mixture is just moist enough to hold together. Form dough into two balls, one about 2/3 of dough and the other the remaining 1/3 of dough. Wrap each with plastic and flatten into disks. Refrigerate at least 1 hour and up to 2 days before rolling out and baking.
Lightly flour a work surface and remove the plastic wrap from the larger dough ball. Using a lightly floured rolling pin, roll out the dough ball to a 12-by-16-inch rectangle, dusting with flour if dough sticks. (Leave smaller dough ball in the fridge.) Transfer rolled-out dough to a 9-by-13-inch baking dish. Carefully line the pan with dough, pressing it into bottom of pan and completely up the sides. Crimp the top edges. Chill dough in fridge until ready to fill.
Roll out remaining dough ball to a 10-by-13-inch rectangle, dusting with flour if dough is sticking. Using a decorative cookie cutter (like apples, leaves or hearts), cut out dough shapes. Reroll scraps if necessary to use up as much dough as possible. Transfer cutouts to a small baking sheet. Return baking pan and sheet to refrigerator to chill while you prepare filling.
Heat oven to 425 degrees. Arrange a wire rack in the lowest position in the oven. Place a large rimmed baking sheet on the floor of the oven to preheat.
Make the filling: In a large bowl, combine apples, sugar, maple syrup, cranberries, tapioca, rum, lemon zest and juice, ginger, salt, cinnamon and nutmeg. Let mixture stand 10 minutes. Pour filling into bottom pie crust and dot with 2 tablespoons diced butter. Arrange dough cutouts on top of apple mixture, overlapping it slightly and making sure several cutout edges touch sides of pan. Whisk together egg and cream. Brush over crust; sprinkle with Demerara sugar.
Move rimmed baking sheet from oven floor to lowest rack. Place pie pan on baking sheet and bake for 20 minutes. Reduce oven temperature to 375 degrees. Continue baking until crust is golden brown and juices are bubbling thickly, 40 to 60 minutes longer. Loosely tent top of pie with foil if crust browns before filling is ready. Transfer pie to a wire rack to cool completely before serving.