In a large bowl, whisk together the flour and salt. Cut in the cold butter until the mixture resembles coarse crumbs. Gradually add ice water, mixing until a dough forms. Divide the dough in half, flatten into discs, wrap, and chill for at least 30 minutes.

Preheat oven to 425°F (220°C). On a lightly floured surface, roll out one disc of dough into a 12-inch circle. Carefully transfer the dough to a 9-inch pie plate, trimming any excess and crimping the edges as desired.

In a large bowl, combine the sliced apples, granulated sugar, flour, cinnamon, nutmeg, and lemon juice. Mix gently until the apples are evenly coated.

Pour the apple mixture into the pie crust. Dot the top of the filling with the small pieces of unsalted butter.

Roll out the second disc of dough and place it over the apple filling. Trim, seal, and crimp the edges of both crusts together. Cut several slits in the top crust to allow steam to escape.

Brush the top crust with the beaten egg wash and sprinkle with granulated sugar. Bake for 15 minutes, then reduce the oven temperature to 375°F (190°C) and bake for an additional 35-45 minutes, or until the crust is golden brown and the filling is bubbly. Let the pie cool completely on a wire rack before serving.