Extra-virgin coconut oil is a great substitute for butter in both the pie dough and the apple filling to make this all-American fruit pie vegan-friendly. We use a mix of apples for the filling: The Golden Delicious keep their shape and are a nice contrast to the soft McIntoshes, and the Granny Smiths give a nice tartness.
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Put the flour, sugar, vinegar and 1/2 teaspoon salt in a food processor, and pulse to combine. Add the coconut oil in small spoonfuls, and pulse until the largest pieces are pea-size. Add 8 tablespoons ice water, and pulse until evenly combined. Squeeze a handful of the dough together; it should just hold its shape. If the mixture is very powdery, pulse in an additional 1 to 2 tablespoons ice water. 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.
Meanwhile, peel and core the apples; cut into 1/2-inch-thick slices. Toss with the sugar and lemon juice in a large bowl. Melt the coconut oil in a large skillet over medium-high heat. Add the apples and cook, stirring occasionally, until the firmer apples soften but hold their shape, about 12 minutes. Add the flour, cinnamon and 1/4 teaspoon salt, and stir to combine. Remove from the heat, and let cool completely. (The filling can be made up to 2 days ahead; cover and refrigerate.)
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). 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. If the dough gets too warm, refrigerate it to firm it up. Ease the crust into a 9 1/2-inch deep-dish pie pan. Add the cooled filling, mounding it slightly in the center.
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. Fold the overhanging dough under itself, and crimp as desired. Brush the top and edges with the almond milk, and sprinkle generously with sugar. Pierce the top with a knife (or make decorative cutouts) a few times to let steam escape. Chill for at least 1 hour.
Position an oven rack in the lowest position in the oven, place a baking sheet on the rack and preheat to 425ºF; preheat for at least 30 minutes. Place the pie on the hot baking sheet, and lower the oven to 375ºF. Bake until the pie is golden and the filling is bubbly, 1 hour to 1 hour 20 minutes, rotating as needed. (Cover the edges with foil if they brown too quickly.) Transfer to a rack, and cool until set, about 3 hours.