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Special equipment: a 9 1/2-inch deep-dish pie pan
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For the dough: Put the flour, sugar, vinegar and 1/2 teaspoon salt in a food processor, and pulse to combine.
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Add the coconut oil in small spoonfuls, and pulse until the largest pieces are pea-size.
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Add 8 tablespoons ice water, and pulse until evenly combined.
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Squeeze a handful of the dough together; it should just hold its shape.
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If the mixture is very powdery, pulse in an additional 1 to 2 tablespoons ice water.
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Divide the dough between 2 large pieces of plastic wrap, pat each into a 1/2-inch thick discs and chill for at least 1 hour up to overnight.
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For the filling: Meanwhile, peel and core the apples; cut 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 the coconut oil 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, about 12 minutes.
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Add the flour, cinnamon and 1/4 teaspoon salt, and stir to combine.
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Remove from the heat, and let cool completely.
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(The filling can be made up to 2 days ahead; cover and refrigerate.)
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To assemble: To make rolling easier, let the dough soften a bitit should be slightly soft when pressedat room temperature (this may take anywhere from 20 to 40 minutes depending on the temperature of your kitchen).
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Roll 1 disc of dough out into a 13-inch round on a lightly floured surface or between two 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 the crust into a 9 1/2-inch deep-dish pie pan.
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Add the cooled filling, mounding it slightly in the center.
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Roll out the remaining dough disc into a 12-inch round; place it over the filling, and press the 2 crusts together around the edges.
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Fold the overhanging dough under itself, and crimp as desired.
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Brush the top and edges with the almond milk, and sprinkle generously with sugar.
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Pierce the top with a knife (or make decorative cutouts) a few times to let steam escape.
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Chill for at least 1 hour.
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Position an oven rack in the lowest position in the oven, place a baking sheet on the rack and preheat to 425 degrees F; preheat for at least 30 minutes.
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Place the pie on the hot baking sheet, and lower the oven to 375 degrees F. Bake until the pie is golden and the filling is bubbly, 1 hour to 1 hour 20 minutes, rotating as needed.
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(Cover the edges with foil if they brown too quickly.)
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Transfer to a rack, and cool until set, about 3 hours.
