01 - In a large bowl, combine flour, salt, and sugar. Add cold butter and cut in using a pastry blender or fork until mixture resembles coarse crumbs. Gradually add ice water, one tablespoon at a time, mixing until dough forms. Divide dough in half, shape into disks, wrap in plastic, and chill for at least 1 hour.
02 - In a large bowl, toss sliced apples with granulated sugar, brown sugar, flour, lemon juice, cinnamon, nutmeg, and salt. Let rest to release juices while rolling out dough.
03 - Set oven temperature to 400°F.
04 - On a lightly floured surface, roll one dough disk to fit a 9-inch pie plate. Line pie plate with dough, leaving an overhang.
05 - Pour apple mixture into crust and dot with butter pieces.
06 - Roll second dough disk and place over filling. Trim excess dough and crimp edges to seal. Cut a few slits on top for ventilation.
07 - Combine beaten egg with milk and brush evenly over crust. Sprinkle coarse sugar if desired.
08 - Bake at 400°F for 20 minutes.
09 - Reduce oven temperature to 350°F and bake for an additional 35 to 40 minutes until crust is golden and filling bubbles.
10 - Allow pie to cool on a wire rack for at least 2 hours before slicing.