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1
For The Pie Dough: In the bowl of a food processor fitted with the metal blade, process 3/4 cup flour, salt, and sugar until combined, about two 1-second pulses. Add butter and shortening and process until dough just starts to collect in uneven clumps, about 10 seconds; dough will resemble cottage cheese curds and there should be no uncoated flour. Scrape bowl with rubber spatula and redistribute dough evenly around processor blade. Add remaining 1/2 cup flour and pulse until mixture is evenly distributed around bowl and mass of dough has been broken up, 4 to 6 pulses. Transfer mixture into medium bowl.
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2
Sprinkle vodka and water over mixture. Using a folding motion, use a rubber spatula to mix, pressing down on dough until dough is slightly tacky and sticks together. Flatten the dough into 4-inch disk. Wrap in plastic wrap and refrigerate at least 45 minutes or up to 2 days.
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3
Remove dough from refrigerator and roll out on floured work surface to 12-inch circle, about 1/8 inch thick. Roll dough loosely around rolling pin and unroll into a 9-inch pie plate, leaving at least 1-inch overhang on each side. Working around circumference, ease dough into plate by gently lifting edge of dough with one hand while pressing into plate bottom with other hand. Leave dough that overhangs plate in place; refrigerate until dough is firm, about 15 minutes.
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4
Adjust oven rack to lowest position, place rimmed baking sheet on rack, and heat oven to 400 degrees. Remove pie pan from refrigerator and trim overhang to 1/2 inch beyond lip of pie plate. Fold overhang under itself; folded edge should be flush with edge of pie plate. Using thumb and forefinger, flute edge of dough. Refrigerate until firm, about 15 minutes.
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5
Remove pie shell from refrigerator and press a doubled 12-inch piece of aluminum foil inside the pie shell, and fold the edges of the foil to shield the fluted edges. Evenly distribute 2 cups of ceramic or metal pie weights over foil. (you can also use dried beans or pennies if you have no pie weights). Bake on rimmed baking sheet for 15 minutes. Carefully, remove foil and weights by gathering sides of soil and pulling up and out. Place pie shell back into the oven and continue baking until lightly golden brown, about 5 to 10 minutes more. Remove from oven, and set aside while preparing the filling.
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6
Lower oven temperature to 275 degrees. Place pie shell in oven if not still warm.
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7
In a medium heatproof bowl set in skillet of water maintained at just below simmer, melt butter. Remove bowl from skillet; mix in sugar and salt until butter is absorbed. Beat in eggs, then corn syrup and vanilla. Return bowl to hot water; stir until mixture is shiny and warm to the touch, about 130 degrees. Remove from heat; stir in pecans.
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8
Pour mixture into warm shell and scatter chocolate pieces over pecan mixture; gently press the chocolate into the filling with the back of a spoon. Bake until center feels set yet soft, like gelatin, when gently pressed, 50 to 60 minutes. Transfer pie to rack; let cool completely, at least 4 hours. Serve pie at room temperature or warm, with lightly sweetened whipped cream or vanilla ice cream.
