Mix flour, sugar, and salt. Cut in cold butter until pea-size crumbs form, then add ice water 1 tablespoon at a time until the dough just holds together. Divide into two disks, wrap, and chill for at least 1 hour.
Toss apple slices with both sugars, cinnamon, nutmeg, salt, and lemon juice. Rest 25 to 30 minutes, then drain the released liquid into a small saucepan.
Simmer the drained liquid over medium heat for 5 to 7 minutes until glossy and syrupy. Cool 5 minutes, then toss with the apples and cornstarch.
Place a rimmed baking sheet on the lower-middle rack and preheat the oven to 425°F. Roll one dough disk to about 12 inches and ease it into a 9-inch pie plate. Chill 10 minutes. Spoon in the filling, mounding it slightly in the center, and dot with butter. Roll the second disk, lay it over the filling, trim, and crimp the edges. Cut 5 vents and brush with egg wash. Add coarse sugar if using.
Bake on the preheated sheet at 425°F for 20 minutes, then reduce to 375°F and bake 45 to 55 minutes more, until the crust is deep golden and thick bubbles rise through the center vents. Cover the rim with foil if it browns too fast.
Transfer to a wire rack and cool for at least 3 hours before slicing.
