01 - Preheat oven to 400°F. Line a 10x15-inch rimmed baking sheet with parchment paper or lightly grease with butter.
02 - In a large bowl, whisk together flour, sugar, and salt. Add cold cubed butter and cut into the dry ingredients using a pastry blender or your fingers until coarse crumbs form. Gradually add ice water, 1 tablespoon at a time, mixing just until the dough comes together. Divide dough into two pieces, making one slightly larger than the other.
03 - On a lightly floured surface, roll out the larger dough piece into a rectangle to fit the bottom and sides of your prepared pan. Gently lift the dough into the pan and press it evenly against the bottom and up the sides.
04 - In a large bowl, combine sliced apples, granulated sugar, brown sugar, cinnamon, nutmeg, salt, cornstarch, and lemon juice. Toss until apples are evenly coated.
05 - Spread the apple mixture evenly over the bottom crust. Roll out the remaining dough to form the top crust. Place over the apples. Trim excess dough, pinch edges to seal, and cut 4-5 small slits in the top to allow steam to escape.
06 - Whisk together egg and milk in a small bowl. Brush the mixture evenly over the top crust using a pastry brush. Sprinkle with coarse sugar if desired.
07 - Bake for 35-40 minutes until the crust is deep golden brown and the filling is bubbling through the vents. If the crust browns too quickly, tent loosely with foil.
08 - Let the pie cool for at least 30 minutes before slicing into squares. Serve warm or at room temperature with vanilla ice cream or whipped cream.