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. Carefully fit into a 9-inch pie dish and trim excess edges from the rim.
04 - Pour apple mixture into the prepared crust and dot the top with small pieces of butter.
05 - Roll the second dough disc into a 12-inch round and place over the apples. Trim excess dough, fold edges under, and crimp to seal. Cut several small slits in the top crust to allow steam to escape during baking.
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 pie for 20 minutes. Reduce oven temperature to 375°F and continue baking for 35-40 minutes until crust is golden brown and filling is bubbly.
08 - Transfer pie to a wire rack and let cool for at least 2 hours before slicing to allow filling to set.