Combine flour and salt in a large bowl, then cut in the cold butter until pea-sized crumbs form.

Gradually add ice water, mixing until the dough just comes together, then divide in half and chill for 30 minutes.

In a large bowl, toss sliced apples with sugar, cinnamon, nutmeg, lemon juice, and flour until evenly coated.

Roll out one dough half into a 12-inch circle and place it in a 9-inch pie plate.

Pour the apple filling into the crust.

Roll out the second dough half and place it over the filling, then trim and crimp the edges to seal.

Cut several slits in the top crust for ventilation and brush with the egg wash.

Preheat oven to 425°F (220°C) and bake for 15 minutes.

Reduce oven temperature to 375°F (190°C) and continue baking for 35-45 minutes, or until the crust is golden brown and the filling is bubbling.

Let the pie cool completely on a wire rack before slicing and serving.