3 cups all-purpose flour, plus more for work surface
3/4 cup cold unsalted butter, sliced
5 1/2 tablespoons cold vegetable shortening,slice
1 1/2 tablespoons granulated sugar
1 teaspoon kosher salt
6 to 8 tablespoons ice-cold water
Roasted Apple Filling
5 Pounds Granny Smith Apples, peeled, sliced into 1/2-inch wedges
3/4 cup granulated sugar
1/4 cup all-purpose flour, divided
1/2 cup packed light brown sugar
1 teaspoon ground cinnamon
1/4 teaspoon ground nugmeg
1/2 teaspoon kosher salt
3 teaspoons unsalted butter, cut in small pieces
1 large egg
Directions
Prepare the crust: Pulse first 5 ingredients in a food processor until mixure resembles coarse meal, 5 to 6 times. While pulsing, graduallyadd ice-cold water, 1 taablespoon at a time, pulsing just until dough begins to come together. Divide dough in half; shape into 2 flat disks. Wrap each in plastic wrap, chill 2 hours or up to 2 days.
Preheat the oven to 375*F. Toss together apples, granulatted sugar, and 2 tablespoons of the flour in the bowl until well coated. Divide apples between 2 large parchment paper-lined rimmed baking sheets. Bake until just tender, about 30 minutes, rotating baking sheets between top and bottom racks halfway through baking time. Cool 30 minutes. Transfer to bowl. Fold in browwn sugar, cinnamon, nutmeg, salt, and remaining 2 tablespoons flour until combined. Chill 1 hour.
Assemble pie: Unwrap 1 dough disk. Roll out on a lightly floured surface into a 1/4-to 1/8-inch thickness. Fit into a lightly greased (with cooking spray) 9-inch deep-dish pie plate. Repeat rolling procedure with remaining disk. Cut 6 (1 1/4-inch-wide) strips, and set aside. Cut 3 (3/4-inch-wide) strips from remaining dough. Braid thinner strips.
Spoon filling into prepared pie plate, smoothing to form an even surface; dot with butter. Arrange 1 1/4-inch-wide dough strips and the braid in a lattice design over filling. Trim excess dough from edges; fold dough under to create a clean edge. Chill pie 30 minutes.
Preheat over to 350*F. Whisk together egg and 1 tablespoon water until well blended. Brush entire pie with egg wash. Bake on lowest oven rack until crust is golden and filling is bubbly, 1 hour to 1 hour and 20 minutes, shielding pie with aluminum foil after 50 minutes, if needed. Cool on a wire rack 2 hours before serving.