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