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1.In a food processor, pulse 2 1/2 cups of the flour with the salt and 1 teaspoon of sugar.
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Add 8 tablespoons of the butter and the shortening; pulse until the mixture resembles small peas.
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Add 1/3 cup of ice water and pulse until evenly moistened.
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Squeeze some of the mixture with your hand; it should come together.
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If it crumbles, add 1 tablespoon of ice water and pulse again.
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Turn the dough out onto a work surface and gently press with the heel of your hand, then gather into a ball with a few quick strokes.
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Divide in half and form into disks.
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Cover with plastic wrap and refrigerate for at least 30 minutes or for up to 2 days.
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On a lightly floured surface, roll 1 disk into a 13-inch round 1/8 inch thick.
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Fit the round into a 9-inch glass pie plate and trim the overhang to 1/2 inch.
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Refrigerate the pie shell.
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Roll out the second disk into a 12-inch round 1/8 inch thick; transfer to a parchment-lined baking sheet.
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Cover with plastic wrap and refrigerate.
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4.
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Peel, halve and core the apples, then cut into 3/4-inch wedges and toss with the lemon juice in a large bowl.
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In a 12-inch skillet, melt the remaining 8 tablespoons of butter over low heat; stir in the brown sugar.
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Add the apples and turn to coat.
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Increase the heat to high and cook, turning occasionally, until most of the wedges are tender but not mushy, 15 minutes.
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Do not overcook.
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Immediately scoop the apples and their juices onto a rimmed baking sheet.
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Sprinkle the remaining 1 1/2 tablespoons of flour and the cinnamon over them and toss until the flour disappears.
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Place the baking sheet on a wire rack and let the apples cool to room temperature, 40 minutes.
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Preheat the oven to 450.
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Arrange the apples in the pie shell; drizzle the juices over them.
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Moisten the pie rim with a wet pastry brush.
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Center the top crust over the apples and press the rim to seal.
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Using scissors, trim the top crust to a 1/2-inch overhang, then fold it under and crimp.
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Dissolve the remaining 1 teaspoon of sugar in the milk and lightly brush the top of the pie.
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Pierce several holes in the top of the pie with a fork.
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7.
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Bake the pie for 25 minutes, or until the crust is golden brown.
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If the crust begins to brown too quickly, cover the rim with foil.
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Reduce the heat to 375and bake for 20 minutes longer, or until you can hear the apple pie filling bubbling.
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Transfer the apple pie to a wire rack and let cool for at least 1 hour before cutting into wedges and serving.