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1. To make the crust: Whisk together the flour, sugar, and salt in a medium bowl. Cut in the butter with a pastry blender or two knives used scissors-fashion until the butter is the size of small peas. Sprinkle 1 tablespoon of the water over the mixture, stirring with a fork to moisten it evenly. Continue adding water until the dough just begins to come together when a small bit is pressed between your fingers; do not overwork the dough. Press the dough together into a ball and knead lightly. Shape the dough into a disk, wrap in wax paper, and refrigerate for at least 30 minutes, or for up to 2 days.
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2. Position a rack in the middle of the oven and preheat the oven to 425u00b0F.
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3. Roll out the dough on a lightly floured surface to a 12- to 13-inch round. Transfer the dough to a 9-inch glass pie plate and gently press the pastry against the bottom and up the sides of the plate. Turn the overhang under and crimp the edges. Prick the bottom and sides of the shell with a fork.
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4. Line the pie shell with a piece of heavy-duty aluminum foil, pressing it snugly into the bottom and against the sides, and fill with uncooked rice or beans. Bake the crust for 12 minutes. Remove the foil and rice and bake for 8 to 10 minutes longer, or until the crust is golden brown. Let cool to room temperature on a wire rack.
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5. To make the filling: Bring the coconut milk just to a boil in a large heavy saucepan over medium heat. Remove the pan from the heat and cover to keep warm.
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6. Beat the sugar and egg yolks with an electric mixer on medium-high speed in a large deep bowl until very thick and pale and the volume has increased at least three times. Reduce the speed to medium and beat in the flour, cornstarch, and salt, scraping down the sides of the bowl as necessary. While beating, gradually pour in the warm coconut milk. Return the mixture to the saucepan and cook over medium-high heat, whisking constantly, until it comes to a boil and thickens, then boil for 1 minute, whisking constantly. Remove the pan from the heat, add the butter, and whisk until melted. Add 3/4 cup of the coconut and 1/2 teaspoon of the vanilla.
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7. Transfer the pastry cream to a bowl and let cool to room temperature, whisking occasionally. Cover the surface with plastic wrap to prevent a skin from forming and refrigerate for about 2 hours, until thoroughly chilled and set, or for up to 1 day.
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8. Beat the heavy cream with the confectioners' sugar with an electric mixer on medium-high speed in a large deep bowl until it holds stiff peaks when the beaters are lifted. Beat in the remaining vanilla. With a rubber spatula, fold about one-quarter of the whipped cream into the pastry cream.
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9. Transfer the pastry cream to the crust and smooth the top with a small offset spatula. Spread the remaining whipped cream over the top with the clean offset spatula. Refrigerate for at least 30 minutes, or for up to 4 hours, before serving.
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10. Sprinkle the top of the pie with the remaining toasted coconut. Serve cut into wedges.
