Whisk together in a large bowl, flour, sugar, and salt until well blended.
Add in cheese and the cubed butter, use a fork or fingers to break up into flour until the mixture resembles small peas.
Gradually add ice water over the mixture, toss with a fork to moisten dough evenly. Use as few strokes as possible. When dough holds together easily when pressed, stop adding water.
Work the dough into a ball, then divide the dough into two balls, cover with plastic wrap. Refrigerate for 30 minutes.
To Make Pie Filling and Bake Apple Pie:
Preheat the oven to 425°F
In a large bowl, combine apple slices, cheese, white sugar, brown sugar, a small pinch of salt, cinnamon, nutmeg, and cornstarch; stir. Allow standing for 15 minutes and mix in lemon juice and lemon rind.
Unwrap the pastry for the bottom crust. Roll it with a rolling pin and use it to line a 9-inch pie plate.
Brush the bottom of the crust with egg white. Fill with apple mixture (leave the juice) and be sure to create a higher mound of apple slices in the center because apples will cook down as they bake.
Transfer the juice to the skillet, and simmer over medium heat until thickened and lightly caramelized. Stir often to prevent burning.
Pour the juice from skillet over apple slices and top with some cubed butter.
To Make a Lattice Top for a Pie Crust:
Roll remaining crust and cut into twelve ½-inch to ¾-inch wide, depending on how thick you want your lattice strips. Arrange 6 strips across pie. Form lattice by arranging 6 strips diagonally across first strips then gently press ends into crust edges.
Brush the top pie crust with egg yolk then sprinkle with white sugar.
Bake for 15 minutes then lower the temperature to 400°F and continue baking until the crust is golden brown for 35 minutes or longer.
Remove from the heat and enjoy with ice cream vanilla.