For the dough:
2 1/2 cups all-purpose flour
2 tsp. salt
1 Tbs. sugar
6 oz. white cheddar cheese, finely grated
16 Tbs. (2 sticks) cold unsalted butter, cut
into 1/2-inch pieces
1/3 to 1/2 cup ice water
For the filling:
2 lb. Braeburn apples, peeled, cored and cut
into slices 1/4 inch thick
1 1/2 lb. Granny Smith apples, peeled, cored
and cut into slices 1/4 inch thick
3/4 cup sugar
1 Tbs. fresh orange juice
3/4 tsp. ground cinnamon
1/4 tsp. freshly grated nutmeg
1/4 tsp. salt
1 Tbs. unsalted butter
3 Tbs. cornstarch
2 Tbs. heavy cream
To make the dough, in a bowl, combine the flour, salt, sugar and cheese, breaking apart any large clumps of cheese. Put the butter in a separate bowl. Place both bowls in the freezer for 10 minutes.
In a food processor, pulse the flour mixture until the ingredients are combined, about 5 pulses. Add the butter and process until the mixture resembles coarse meal, 15 to 20 pulses. Add 1/3 cup of the ice water and pulse twice. The dough should hold together when squeezed with your fingers but should not be sticky. If it is crumbly, add more water 1 Tbs. at a time, pulsing twice after each addition. Turn the dough out onto a work surface, divide in half and shape each half into a disk. Wrap the disks separately in plastic wrap and refrigerate for 1 hour.
To make the filling, in a large bowl, combine the apples, sugar, lemon juice, cinnamon, nutmeg and salt and stir to combine. Let stand at room temperature for 30 minutes to 1 hour.
Meanwhile, remove 1 of the dough disks from the refrigerator and let stand for 5 minutes. Place the dough between 2 sheets of lightly floured waxed paper and roll out into a 12-inch round about 3/16 inch thick. Brush off the excess flour. Transfer to a pie dish and press the dough into the dish. Trim the edges, leaving a 1/2-inch overhang. Cover with plastic wrap and refrigerate for 30 minutes.
Preheat an oven to 400°F.
Pour the apples into a sieve set over a small saucepan, then transfer the apples to a large bowl. Set the saucepan with the juices over medium-high heat, add the butter and cook until reduced to 1/3 cup, 3 to 5 minutes. Remove from the heat. Sprinkle the cornstarch over the apples and toss to combine, then stir in the reduced juices. Transfer the apples to the pie shell.
Roll out the remaining dough disk into a 12-inch round about 3/16 inch thick. Drape the dough over the apples and press gently to eliminate any air pockets. Trim the dough flush with the rim of the dish. Fold the bottom crust over the top crust and crimp to form a decorative edge. Cut 4 slits in the top of the crust to allow steam to escape. Brush the top of the crust with the cream.
Bake for 20 minutes. Cover the edges and top with aluminum foil if they begin to get too dark. Reduce the oven temperature to 350°F and continue to bake until the apples are easily pierced with a knife, 65 to 70 minutes more. Transfer to a wire rack and let cool for at least 1 1/2 hours before serving. Serves 8 to 12.