Make the pie crust: In a large bowl, mix flour and salt. Cut in chilled butter until mixture resembles coarse crumbs. Gradually add ice water, 1 tbsp at a time, until dough comes together.

Divide dough into two balls, flatten into disks, wrap in plastic, and refrigerate for at least 1 hour.

Prepare filling: In a large bowl, toss apple slices with sugar, lemon juice, cinnamon, and nutmeg until evenly coated.

Roll out one dough disk on a floured surface to fit a 9-inch pie plate. Transfer crust to plate and trim edges.

Add apple filling, mounding slightly in center. Dot with diced butter.

Roll out second dough disk and place over filling. Trim, seal, and crimp edges. Cut slits in top crust to vent.

Brush top crust with beaten egg. Optional: sprinkle with sugar.

Bake at 375°F (190°C) for 45-50 minutes until crust is golden and filling is bubbly. Cool before serving.