Roll out pie crust; fit into a 9-inch, deep-dish pan. Refrigerate until ready to use.

Place cheese, flour, sugar, and salt in a food processor; stir. Pulse in butter, forming large chunks. Add milk and pulse just until dough holds together. Collect dough into a ball and flatten into a thick disk. Wrap in plastic and refrigerate for 30 minutes.

Preheat oven to 425°. Peel and thinly slice apples. Transfer to a large bowl and toss with lemon zest and juice. Stir in spices, sugar, and flour; toss until coated. Remove pie plate from fridge; pour in apple mixture.

Roll out cheesy dough and fit over top of pie. Trim and flute edges. Cut 5 steam vents, about 1½ inches long, in crust. Bake for 20 minutes. Reduce heat to 350° and bake 40–45 minutes more, until crust is brown and filling is bubbly. Check crust and cover lightly with foil if it’s getting too brown. Serve warm (reheat at 350° for 20 minutes).