In a large mixing bowl, combine 4 cups of all-purpose flour with 1 teaspoon of salt. Cut in 1 cup of chilled unsalted butter until the mixture resembles coarse crumbs.

Gradually add 1/2 cup of cold water, mixing until a dough forms. Divide the dough in half, shape into disks, wrap tightly, and refrigerate for at least 1 hour.

Preheat your oven to 375°F (190°C). Prepare a 15x10-inch baking pan by greasing it or lining it with parchment paper.

On a floured surface, roll out one disk of dough to fit your baking pan. Carefully press the rolled dough into the corners and up the sides of the pan.

In a large bowl, combine 10 cups of thinly sliced apples, 1 1/2 cups of granulated sugar, 1/2 cup of light brown sugar, 2 teaspoons of ground cinnamon, and 1/4 teaspoon of ground nutmeg. Add 3 tablespoons of flour and 2 tablespoons of lemon juice and toss until evenly coated.

Spread the apple filling evenly over the dough. Roll out the second disk to cover the filling, sealing the edges tightly. Cut slits in the top crust and brush with beaten egg.

Bake for 45-50 minutes until the crust is golden brown and the filling bubbles. Cover edges with foil if browning too quickly.

Allow to cool completely before slicing into squares and serving.