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

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

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

Roll out one dough disk on a floured surface to fit a 9-inch pie dish. Place the crust in the dish and trim the edges.

Add the apple filling, dot with diced butter, then roll out the second dough disk and place it over the filling. Trim and crimp the edges to seal.

Cut slits in the top crust for ventilation, brush with beaten egg, and optionally sprinkle with sugar.

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