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 your fingers until coarse crumbs form. Gradually add ice water, mixing just until dough comes together. Divide dough into two portions, making one piece slightly larger for the bottom crust.
03 - On a lightly floured surface, roll out the larger dough portion to fit the bottom and sides of the prepared baking sheet. Carefully transfer dough to pan, pressing evenly 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 - Pour apple mixture evenly over the bottom crust. Roll out remaining dough and place over apples. Trim excess dough, pinch edges to seal top and bottom crusts together, and cut several small slits in the top crust to allow steam to escape during baking.
06 - Whisk together egg and milk in a small bowl. Brush mixture evenly over the top crust. Sprinkle with coarse sugar if desired for added texture and sweetness.
07 - Bake for 35 to 40 minutes, or until the crust is deep golden brown and the filling is bubbling actively through the steam vents.
08 - Allow pie to cool for at least 30 minutes before slicing into squares. This resting period helps the filling set for cleaner cuts. Serve warm or at room temperature.