01 - Whisk flour, salt, and sugar in a large bowl. Cut in cold butter with 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 chill for at least 1 hour.
02 - Toss sliced apples with granulated sugar, brown sugar, flour, lemon juice, cinnamon, nutmeg, cloves, and salt in a large mixing bowl 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.
04 - Pour apple mixture into crust and dot with butter pieces.
05 - Roll second dough disc into a 12-inch round. Place over apples. Trim, fold, and crimp edges to seal. Cut several small slits in top for steam to escape.
06 - Beat egg with milk and brush over 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 and filling is bubbly.
08 - Let pie cool on a wire rack for at least 2 hours before slicing to allow filling to set.