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