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, 1 tablespoon sugar, and 1 1/2 teaspoons salt. Cut in cold butter using a pastry blender or fingers until mixture resembles coarse crumbs. Gradually add ice water, mixing gently until dough just comes together. Divide dough into two portions, with one piece slightly larger than the other. Shape into disks, wrap, and refrigerate for 15 minutes.
03 - On a lightly floured surface, roll the larger dough portion into a rectangle to fit the bottom and up the sides of your prepared baking sheet. Carefully transfer dough to pan, pressing gently into corners and edges. Refrigerate while preparing filling.
04 - In a large bowl, combine sliced apples, granulated sugar, brown sugar, cinnamon, nutmeg, 1/4 teaspoon salt, cornstarch, and lemon juice. Toss until apples are evenly coated.
05 - Spread apple mixture evenly over the bottom crust. Roll out remaining dough into a rectangle and place over apples. Trim excess dough, then pinch and seal edges together. Cut 4-5 small slits in top crust to allow steam to escape.
06 - Whisk egg with milk until combined. Brush mixture evenly over top crust. Sprinkle with coarse sugar if desired for extra crunch and shine.
07 - Bake for 35-40 minutes until crust is deep golden brown and filling is bubbling actively through vent slits. If edges brown too quickly, cover with foil strips during last 10 minutes.
08 - Allow pie to cool for at least 30 minutes before slicing into squares. This allows filling to set for cleaner cuts. Serve warm or at room temperature.