01 - Whisk flour, salt, and sugar in a large bowl. Cut in cold butter using a pastry cutter or fingers until mixture resembles coarse crumbs. Gradually add ice water, mixing until dough just comes together. Divide dough in half, flatten into discs, wrap in plastic, and refrigerate for at least 1 hour.
02 - Combine sliced apples with granulated sugar, brown sugar, flour, lemon juice, cinnamon, nutmeg, cloves, and salt in a large mixing bowl. Toss until apples are evenly coated. Set aside.
03 - On a floured surface, roll one dough disc into a 12-inch round. Fit into a 9-inch pie dish and trim excess edges.
04 - Pour apple mixture into the crust and dot with small pieces of butter.
05 - Roll second dough disc into a 12-inch round and place over apples. Trim, fold, and crimp edges to seal. Cut several small slits in the top crust to allow steam to escape.
06 - Beat egg with milk and brush mixture over the top crust. Sprinkle with coarse sugar if desired.
07 - Preheat oven to 425°F. Bake for 20 minutes, then reduce temperature to 375°F and continue baking for 35-40 minutes until crust is golden and filling is bubbly.
08 - Let pie cool on a wire rack for at least 2 hours before slicing to allow filling to set.