01 - Preheat oven to 400°F. Line a 10x15-inch rimmed baking sheet with parchment paper or lightly grease with cooking spray.
02 - In a large bowl, combine flour, sugar, and salt. Cut in cold butter until coarse crumbs form. Gradually add ice water, just until dough comes together. Divide dough in two portions, with one piece slightly larger.
03 - Roll out the larger dough piece on a floured surface to fit the bottom and sides of the prepared pan. Gently lift into the pan and press evenly into corners and edges.
04 - In a large bowl, toss together sliced apples, both sugars, cinnamon, nutmeg, salt, cornstarch, and lemon juice until apples are evenly coated.
05 - Pour apple mixture evenly over bottom crust. Roll out remaining dough to form the top crust. Place over apples, trim excess, pinch edges to seal, and cut a few small slits for steam to escape.
06 - Whisk egg with milk and brush evenly over the top crust. Sprinkle with coarse sugar if desired.
07 - Bake for 35 to 40 minutes, until the crust is golden brown and filling is bubbly throughout.
08 - Allow to cool for at least 30 minutes before slicing into squares. Serve warm or at room temperature with vanilla ice cream or whipped cream.