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1
Preheat oven to 350u00b0F. Roll pie crust out on a lightly-floured work surface to a circle roughly 12 inches in diameter. Transfer to a plate, rolling up overhanging edge and refrigerate for 30 minutes. Whisk egg with cream. Transfer to a 9-inch pie plate, then, using kitchen shears or a paring knife, trim crust around edge of pie plate. Crimp crust edge, then brush crimped edge with egg wash and sprinkle with demerara sugar (do not brush or sugar bottom of crust or wax paper will stick to it). Line bottom of crust with a round of wax paper, add dried beans or pie weights, and bake crust until edge is golden, about 15 minutes. Remove weights and wax paper and bake crust until bottom and side is golden, about 5 minutes longer. Let cool slightly.
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2
Peel apples partially in a spiral pattern, starting at the stem and proceeding towards the bottom, removing about half the skin while leaving a stripe of skin on each apple. Core apples and cut into 1/4-inch slices. Toss apple slices with lemon juice in a large mixing bowl.
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3
In a small bowl, mix butter with flour to form a smooth paste.
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4
Add butter-flour mixture, brown sugar, granulated sugar, cinnamon, ginger, salt, allspice, and nutmeg to apples and stir to combine. Scrape apple mixture into a large, wide-bottomed pot and heat over medium heat, stirring occasionally, until apples are soft but not falling apart, about 20 minutes. Allow apples to cool slightly, then scrape into pre-baked pie crust.
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5
While apples are cooling, place granulated sugar, butter, heavy cream, corn syrup, maple syrup, bourbon, molasses, and salt in a heavy-bottomed saucepan and cook over medium heat, stirring, until ingredients are fully combined, about 2 minutes. Stop stirring, turn heat to medium high, and cook until mixture reaches 236u00b0F on a candy thermometer, about 5 minutes. Off the heat, allow caramel to cool to 190 degrees, about 3 minutes. Mix in toasted pecans, then spoon the caramel-pecan mixture over the apples, patting and shaping to form an even coating. (If you don't want to use all the caramel pecan mixture on top of the pie, any leftovers can be spooned onto a lined baking sheet and cooled to make turtles.) Let pie cool to room temperature, then slice and serve.
