WHAT YOU'LL NEED
FOR THE CRUST (make 2, separately, one for bottom crust, one for the lattice top):
1 1/3 cups unbleached all-purpose flour, plus extra for rolling out dough
1 tablespoon confectioners' sugar
1/2 teaspoon salt
5 tablespoons vegetable shortening, cut into small pieces and chilled for at least 15 minutes
5 tablespoons unsalted butter, cut into 1/4-inch pieces and chilled for at least 15 minutes
1 large egg white
2 tablespoons ice water
1 1/2 teaspoons white vinegar
FOR THE FILLING
3 tablespoons unsalted butter
5 pounds Granny Smith apples, peeled, cored and cut into 1/4-inch slices
3/4 cup granulated sugar
1/4 teaspoon ground cinnamon
1/4 teaspoon salt
1 tablespoon lemon juice
1 egg, lightly beaten
Sanding sugar for sprinkling
1. Combine flour, sugar, and salt in the workbowl of a food processor and pulse several times to blend. Add shortening and pulse 8 to 10 times, until mixture resembles coarse meal. Add butter and pulse another 8 to 10 times, until mixture once again resembles coarse meal.
2. Beat together egg white, water and vinegar in a small bowl; then pour over flour mixture. Pulse 5 to 7 times, until dough just begins to come together in large clumps. If it doesn't stick together, sprinkle another tablespoon of water over mixture and pulse again. Remove lid of food processor and press some dough between your fingers. If it is still very crumbly, process once or twice more.
3. If it holds its shape, press it into a 5-inch disk, wrap in plastic, and refrigerate for at least 2 hours and up to 2 days. Make second pie crust; refrigerate.
4. On a lightly floured countertop, press the disk into a rough circle by pushing down on it all over with the rolling pin. When you have a circle measuring 6 or 7 inches in diameter, use a lightly floured rolling pin to roll out the dough, sliding a large metal spatula underneath the dough after every 4 or 5 strokes to loosen the dough from the work surface, and rotate the dough 45 degrees. Continue to roll, loosen and turn, until you have a 13-inch circle (smaller than this and you might have trouble creating a nice, thick edge).
5. Loosely fold your dough circle around the rolling pin, lift the pin and unroll the dough over the 9-inch shallow pie plate. Gently press it into the bottom and sides with your fingertips, taking care not to stretch or thin the dough when you do this, or dimple it with your fingers, which may cause the dough to shrink in the oven.
6. Use a pair of scissors to trim the crust all around so that it overhangs the edge of the pan by 1 inch. Tuck that extra dough underneath itself to form a double-thick edge that sits on the rim of the pie plate.
7. Pinch the edge of the crust with the thumb and forefinger of one hand while pressing from the inside with the index finger of the other hand, repeating all the way around the edge. Loosely cover with plastic wrap and refrigerate at least 30 minutes before using.
8. To start the filling, melt the butter over medium heat in a large pot. Add apples, sugar, cinnamon, salt and lemon juice; cook, stirring frequently, until apples are cooked through but still hold their shape, about 15 minutes. Use a slotted spoon to transfer the apples to a baking sheet to cool completely. (Filling can be chilled, transferred to an airtight container and refrigerated for up to 1 week.) Spoon the apples into pie shell.
9. Adjust oven rack to lower-middle position and place a rimmed baking sheet on rack. Preheat oven to 425 degrees. Slide the chilled lattice from the parchment onto the pie, adjusting the strips so they are straight and even. Trim the strips so they overhang the rim of the pie by 1 inch. Pinch the ends of the strips so they form part of the rim.
10. Brush the lattice and rim with the beaten egg. Place the pie on the preheated baking sheet and bake for 25 minutes. Lower the heat to 375 degrees and continue to bake until the lattice and rim are golden brown, another 30 to 40 minutes. Cool completely on a wire rack and serve.
11. For the lattice top, repeat step 4, and roll dough into a 13-inch circle. Using a ruler and a fluted pastry wheel or sharp paring knife, cut the dough into eight 1-inch-wide strips.
12. Line up half of the strips vertically, 1 inch apart, on a baking sheet lined with parchment paper. Then gently weave in the horizontal strips.
13. Loosely cover with plastic wrap and refrigerate for at least 30 minutes.