01 - Preheat oven to 400°F. Line a 10x15-inch rimmed baking sheet with parchment paper or lightly grease with butter.
02 - Combine flour, sugar, and salt in a large bowl. Cut in cold butter using a pastry cutter or fingers until coarse crumbs form. Gradually drizzle in ice water, mixing just until dough holds together. Divide dough into two portions, making one slightly larger than the other.
03 - On a lightly floured surface, roll out the larger dough portion 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 thoroughly to coat apples evenly.
05 - Spread apple mixture evenly over the bottom crust. Roll out remaining dough to form top crust. Place over apples, trim excess edges, pinch firmly to seal bottom and top crusts together. Cut several small slits in top crust for steam ventilation.
06 - Whisk together egg and milk until combined. Brush mixture evenly over top crust using a pastry brush. Sprinkle with coarse sugar if desired for extra texture and sweetness.
07 - Bake for 35 to 40 minutes until crust turns deep golden brown and filling bubbles visibly through steam vents. If edges brown too quickly, cover with foil strips during final minutes.
08 - Allow pie to cool for at least 30 minutes before cutting. This ensures filling sets properly. Slice into squares and serve warm or at room temperature.