01 - Combine flour, salt, and sugar in a large bowl. Cut in cold butter with a pastry blender or fork until coarse crumbs form. Gradually add ice water one tablespoon at a time, mixing until dough holds together. Divide dough, shape into disks, wrap, and chill for at least 1 hour.
02 - In a large bowl, toss apples with granulated sugar, brown sugar, flour, lemon juice, cinnamon, nutmeg, and salt. Set aside to release juices while rolling out the dough.
03 - Heat oven to 400°F (200°C).
04 - On a lightly floured surface, roll one dough disk to fit a 9-inch pie plate. Line the plate with dough, leaving an overhang.
05 - Fill the crust with the apple mixture and dot with butter pieces.
06 - Roll out second dough disk and cover apples. Trim excess dough, crimp edges to seal, and cut slits for steam to escape.
07 - Brush beaten egg mixed with milk over crust. Optionally, sprinkle with coarse sugar.
08 - Bake at 400°F (200°C) for 20 minutes. Reduce heat to 350°F (175°C) and bake an additional 35 to 40 minutes until crust is golden and filling bubbles.
09 - Allow pie to cool on a wire rack for at least 2 hours before slicing.