In a food processor bowl, mix the flour, flour, sugar, and salt together.. Pulse for 5 seconds, until briefly combined.
Add the cold butter and pulse until a fine meal forms.
Add the cheese and pulse a few times to just combine.
Transfer to a large bowl and add 5 tbsp. ice water. Using a fork, mix gently until clumps form. Add more water by the tablespoon as needed.
Gather the dough into a ball and divide in half. Shape each half into a disk, wrap in plastic, and store for at least an hour.
To make the filling:

Preheat the oven to 400 degrees.
Mix the cornstarch and sugar until there are no lumps.
Add the apples, lemon juice, zest, and salt. Toss to combine.
To assemble pie:

Lightly flour a work surface and roll out one of the disks into a 13 inch round. Carefully transfer dough to a 9 inch deep-dish pie dish. Brush the edge and overhang with water.
Add the filling to the bottom of the dough lined pie dish. Add the butter in dots to the filling.
Roll out the second dough disk into a 12 inch round and place on top of the filling.
Press the edges together to seal and cut any overhang to 1/2 inch. Crimp the edges decoratively with two fingers.
Using a sharp knife, cut 3 slits in the top of the crust.
Place pie in a foil lined baking sheet and bake for 30 minutes, until the top is golden brown. Remove the pie and carefully cover the edge of the pie crust with aluminum foil to prevent burning.
Reduce oven temperature to 375 degrees, place pie in oven and bake for additional 30 minutes.
Remove to a wire rack and cool for 1 hour.