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 - Roll one dough disc into a 12-inch round on a floured surface. Fit into a 9-inch pie dish, trimming excess edges from the rim.
04 - Pour apple mixture into the prepared crust. Dot the top with small pieces of butter.
05 - Roll remaining dough disc into a 12-inch round. Place over apples. Trim, fold, and crimp edges to seal. Cut several small slits in top crust to allow steam escape during baking.
06 - Beat egg with milk. Brush mixture evenly over top crust. Sprinkle with coarse sugar if desired.
07 - Preheat oven to 425°F. Bake for 20 minutes. Reduce 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 cool for at least 2 hours before slicing to allow filling to set.