Special equipment: A deep 9 1/2-inch pie pan
For the pie dough: Pulse the flour, 4 tablespoons of the butter, the lard, sugar and salt in a food processor until the mixture has the consistency of a fine meal. Add the remaining 8 tablespoons butter, and pulse until you have pea-sized pieces. Sprinkle the vodka and water over the mixture, and pulse until the dough just comes together. Evenly divide the dough between 2 pieces of plastic wrap, and gently press or pat into rounds. Wrap tightly, and refrigerate until firm, about 1 hour up to overnight. (The dough can be frozen for up to 2 months.)
For the filling: Peel and core the apples, then cut them into 1/2-inch-thick slices. Toss with the sugar and lemon juice in a large bowl. Melt 4 tablespoons of the butter in a large skillet over medium-high heat. Add the apples, and cook, stirring occasionally, until the firmer apples soften but hold their shape, 15 to 18 minutes. (The softer apples, like McIntosh, will get very soft and saucy.) Add the flour, cinnamon, cream and salt, and stir until the juices thicken, about 2 minutes. Remove from the heat, and let cool completely. (The filling can be refrigerated, covered, up to 2 days ahead.)
To assemble: Roll out 1 disk of dough into a 13-inch round on a lightly floured surface or between 2 pieces of floured parchment or wax paper. (If the dough gets too warm, refrigerate it to firm it up.) Ease it into a deep 9 1/2-inch pie pan. Mound the cooled filling slightly in the center of the dough, and dot with the remaining 2 tablespoons butter.
Roll out the remaining disk of dough into a 12-inch round. Place it over the filling, and press the 2 crusts together around the edge. Fold the overhanging dough under itself, and crimp as desired. Brush the top and edges with heavy cream, and sprinkle generously with sugar. Pierce the top with a knife a few times (or make decorative cutouts) to let steam escape. Refrigerate at least 1 hour.
To bake: Position an oven rack in the bottom slot of the oven, set a baking sheet on it and preheat to 425 degrees F for at least 30 minutes. Place the pie on the hot baking sheet, and lower the heat to 375 degrees F. Bake until the pie is golden and the filling is bubbly, 1 hour 10 minutes to 1 hour 20 minutes, rotating as needed. (Cover the edge of the crust with foil if it browns too quickly.) Transfer to a rack, and let cool until set, 3 hours.
Serve the cooled pie, or wrap it tightly in foil, label and date, and freeze for up to 2 weeks. Warm it in a 350-degree-F oven for 20 minutes before serving.
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