For the crust: In a food processor, mix the flour, sugar, and salt and blend for 5 seconds. Add the chilled butter and pulse until the dough looks like fine meal. Add the cheese and pulse 5 times. Transfer the mixture to a large bowl and sprinkle with 5 tablespoons of ice water. Use a fork to fluff the mixture until moist clumps form. Add more ice water by the tablespoonful if the mixture is dry. Gather the dough into a ball and divide in half. Shape each half into a disk. Wrap in plastic and chill at least 1 hour.
For the filling: Preheat the oven to 400 degrees F. In a large bowl, mix the cornstarch and sugar, making sure there are no lumps in the cornstarch. Mix in the apples, lemon juice, zest, and salt.
On a lightly floured surface, roll out 1 of the dough disks into a 13-inch round. Transfer the dough to a 9-inch diameter deep-dish glass pie dish and brush the overhang with water. Pour the filling into the dough-lined dish and dot it with the 2 tablespoons butter. On the same lightly floured surface, roll out the second dough disk into a 12-inch round. Place the dough on top of the filling. Press the overhang of the bottom and top dough pieces together to seal. Cut the overhang to 1/2-inch. Fold the overhang under and crimp decoratively, forming a high-standing rim. Cut 3 (2-inch) slits in the top of the crust to allow steam to escape.
Bake the pie until golden brown, about 30 minutes. Cover the crust edge with foil and reduce the oven temperature to 375 degrees F. Bake the pie until the filling bubbles thickly in the center, about 30 minutes. Cool pie on a rack for 1 hour.