1. **Prepare the Crust:** In a large bowl, mix flour and salt. Cut in the cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs. Gradually add ice water, mixing until the dough comes together. Divide into two disks, wrap in plastic, and refrigerate for at least 1 hour.

2. **Preheat Oven:** Preheat your oven to 425°F (220°C).

3. **Prepare the Filling:** In a large bowl, toss the apple slices with sugar, flour, cinnamon, nutmeg, lemon juice, and a pinch of salt. Allow the flavors to meld while you roll out the dough.

4. **Assemble the Pie:** On a lightly floured surface, roll out one disk of dough into a circle large enough to line a 9-inch pie dish. Transfer the dough into the dish, leaving some overhang. Fill with the apple mixture, mounding slightly in the center.

5. **Top Crust:** Roll out the second disk of dough and lay it over the filling. Trim the excess dough and crimp the edges to seal. Cut a few small slits in the top crust to allow steam to escape.

6. **Egg Wash & Sugar:** Brush the top crust with the beaten egg and sprinkle with a little granulated sugar if desired.

7. **Bake:** Place the pie on a baking sheet and bake in the preheated oven for 20 minutes. Then, reduce the temperature to 375°F (190°C) and bake for an additional 30 minutes, or until the crust is golden and the filling is bubbly.

8. **Cool & Serve:** Allow the pie to cool for at least 2 hours before serving to set the filling.