In a large mixing bowl, whisk together the flour and salt.

Add the chilled and cubed butter to the flour mixture. Use a pastry cutter or your hands to cut the butter into the flour until the mixture resembles coarse crumbs.

Gradually add the ice water to the flour and butter mixture. Mix until the dough comes together. Shape the dough into a disk, wrap it in plastic wrap, and refrigerate for at least 30 minutes.

Preheat your oven to 375°F (190°C).

In a separate bowl, combine the thinly sliced apples, 3/4 cup of granulated sugar, cornstarch, ground cinnamon, ground nutmeg, and lemon juice. Toss until the apples are coated in the mixture.

On a lightly floured surface, roll out the chilled dough into a 12-inch circle. Place the dough in a 9-inch pie dish, pressing it against the bottom and sides.

Pour the apple mixture into the prepared pie crust.

Roll out the remaining dough and cut it into thin strips. Create a lattice pattern on top of the pie by criss-crossing the dough strips.

Trim off any excess dough and press the edges to seal.

Brush the top of the pie with the beaten egg for a golden crust.

Bake the pie for 50-60 minutes, or until the crust is golden brown and the filling is bubbly.

Allow the pie to cool for at least 1 hour before serving.