Cut butter into flour and salt until coarse crumbs form. Gradually add ice water until dough forms. Divide, wrap in plastic, and chill for 1 hour.

Peel and slice apples. Toss with both sugars, lemon juice, cinnamon, nutmeg, and cornstarch. Let sit for 15 minutes.

Roll out one dough disc and fit into a pie dish. Fill with apple mixture. Add butter if desired. Top with second crust, crimp edges, and cut vents or make a lattice.

Brush crust with beaten egg. Bake at 400°F for 20 minutes, then at 350°F for 35–40 minutes until golden and bubbly.

Cool at least 2 hours before slicing to allow filling to set.