3¾ cups all-purpose flour
1 teaspoon salt
1¼ cups cold unsalted butter (2½ sticks), cut into small pieces
6 tablespoons cold vegetable shortening
3 cups Golden Delicious apples, cored, peeled, and sliced
3 cups Granny Smith apples, cored, peeled, and sliced
1 tablespoon fresh lemon juice
¼ cup light-brown sugar
¼ cup granulated sugar
1½ teaspoons ground cinnamon
¼ teaspoon ground nutmeg
1 tablespoon plus 1 teaspoon cornstarch

For the dough:  Place the flour and ¾ teaspoon salt in the bowl of a food processor fitted with a metal blade. Pulse to combine. Add 1 cup plus 2 tablespoons of the butter pieces and the vegetable shortening and pulse 6 to 8 times, until the mixture resembles coarse meal. Sprinkle 4 tablespoons of cold water over the dough and pulse 3 to 4 more times until the dough begins to hold together. Add more water, 1 tablespoon at a time, until the dough holds together. Form the dough into 2 disks, wrap each in plastic wrap, and refrigerate for at least 1 hour.

For the filling: Combine the apples, lemon juice, sugars, cinnamon, nutmeg, and remaining salt in a large bowl and toss. Let sit for at least 30 minutes or up to 2 hours. Drain apples, reserving liquid. Toss apples with cornstarch and set aside. Place ½ cup of the reserved liquid in a small saucepan over medium-high heat, add the remaining butter, bring to a boil, and let cook until the mixture becomes thick and syrupy. Do not stir. Add the syrup to the apples and gently toss to combine.

Heat oven to 425°F. Roll out one disk of dough into a 12-inch round about 1/8-inch thick, on a lightly floured surface. Fit the dough into a 10-inch pie plate. Trim dough, crimp edge, and fill with the apple filling. Roll out the second disk of dough for the top crust and place over the apples to form a top crust. Cut several slits to vent the pie. Bake until the juices bubble through the slits — 45 to 55 minutes. Let cool for at least 4 hours before serving.