Prepare the crust: In a large bowl, combine flour, sugar, and salt. Add the cold butter and mix until the mixture resembles coarse crumbs. Slowly add ice water, 1 tablespoon at a time, until the dough comes together. Divide the dough, shape into disks, wrap in plastic, and refrigerate for 30 minutes.

1. Prepare the filling: Peel, core, and slice the apples. Toss with granulated sugar, brown sugar, flour, cinnamon, nutmeg, lemon juice, and salt. Set aside.
2. Assemble the pie: Preheat the oven to 425°F (220°C). Roll out one disk of dough to fit a 9-inch pie pan. Place in the pan, trim excess dough, and add the apple mixture. Dot with butter. Roll out the second disk and place over the apples. Seal, trim, and crimp the edges. Cut slits in the top crust. Brush with egg wash.
3. Bake: Bake for 45-50 minutes or until the crust is golden and the filling is bubbling. If edges brown too quickly, cover with foil. Let cool for 2 hours before slicing.