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. Cut in cold butter using a pastry blender or fingers until coarse crumbs form. Gradually add ice water, mixing just until dough holds together. Divide dough into two pieces, making one slightly larger than the other.
03 - On a floured surface, roll the larger dough piece to fit the bottom and sides of the prepared pan. Carefully transfer dough to pan, pressing gently into corners 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 apple mixture evenly over the bottom crust. Roll out remaining dough to form top crust. Place over apples, trim excess dough, and pinch edges to seal. Cut several small slits in the top crust to allow steam to escape.
06 - Whisk egg with milk until combined. Brush 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 bubbles through the vent slits.
08 - Let the pie cool for at least 30 minutes before slicing into squares. Serve warm or at room temperature.