For the crust: In a food processor, combine the flour, sugar, salt, cold butter and grated cheese. Cook's Note: This is where you can add a little extra cheese or use extra-sharp Cheddar to deliver that tangy cheesy flavor in every bite. Pulse the processor until the mixture resembles fine sand.
Remove the lid and add the ice water to the mixture. Run the processor just until the mixture rolls itself into a little ball. If the mixture is a bit dry, add more ice water by the tablespoonful until it comes together. Gather the dough into a ball. With a bench scraper, divide the mixture evenly in half. Shape each half into a disk. Wrap each disk in plastic wrap and chill at least 30 minutes. Cook's Note: At this point you can keep the wrapped dough in the refrigerator for a few days or freeze for later use.
For the filling: Preheat the oven to 400 degrees F. In a large bowl, whisk together the cornstarch and sugar, making sure there are no lumps in the cornstarch. Mix in the apples slices, lemon juice and zest and pinch of salt. Toss to coat the apples completely in the mixture. Cook's Note: If you would like to add a beautiful blush color to your filling, add a red-skinned apple like Braeburn to the mix and toss some of the peel into the mixture. The result is a light pink hue that's absolutely gorgeous and delicious!
After the dough has chilled, lightly flour the work surface and roll 1 of the dough disks into a 13-inch round. Carefully place the dough round to a 9-inch diameter deep-dish glass pie dish. Brush the overhang with water. Pour the apple filling into the dough-lined dish and dot it with the diced butter.
For the top crust, roll out the second dough disk on the same lightly floured surface. Roll out the dough into a 12-inch round, slightly smaller than the bottom crust. Carefully place the dough over the mound of apples. Press the overhang of the bottom and top dough pieces together to seal. Cut the excess dough to 1/2 inch and fold under. Crimp the dough under and pinch together. Cut 3 (2-inch) slits in the top of the crust to allow steam to escape. Cook's Note: For an extra-special touch, combine the pie dough scraps, roll out and then cut out shapes, like apples or leaves, and place on the top crust or pie edges. Brush with egg wash and bake.
Bake the pie until golden brown, about 30 minutes. If the edge of the crust browns too quickly, place an edge guard or craft your own out of aluminum foil and place on the pie edge. Reduce the oven temperature to 375 degrees F. Bake the pie until the apple filling starts to bubble up in the center and has thickened, about 30 minutes. Remove the pie from the oven and cool the pie on a rack for 1 hour.