Mix flour, salt, and sugar in a bowl.

Cut in the cold butter until the mixture looks like coarse crumbs.

Add ice water one tablespoon at a time until the dough holds together.

Divide the dough in half, make disks, wrap in plastic, and refrigerate for at least 1 hour.

Preheat your oven to 425°F (220°C).

Toss the sliced apples with both sugars, flour, lemon juice, cinnamon, and nutmeg in a large bowl.

Roll out one disk of dough and place it in a 9-inch pie pan.

Fill the crust with the apple mixture and add pieces of butter on top.

Roll out the second disk and cover the filling. Trim excess dough and crimp the edges to seal.

Cut slits in the top crust for steam to escape and brush with beaten egg.

Bake for 20 minutes at 425°F, then lower the heat to 350°F (175°C) and bake for another 35-45 minutes until golden and bubbly.

Cool for at least 2 hours before slicing.