Mix the flour, salt, and sugar in a large bowl. Cut in the cold butter until the mixture resembles coarse crumbs with some pea-sized pieces remaining. Add ice water a little at a time, mixing just until the dough comes together.

Divide the dough into two portions, shape each into a disk, wrap, and refrigerate until firm.

Place the sliced apples in a large bowl. Toss them with sugar, cinnamon, optional nutmeg, lemon juice, flour or cornstarch, and a pinch of salt. Let the mixture stand briefly.

On a lightly floured surface, roll one pastry disk into a circle large enough to fit a pie dish with a little overhang. Transfer it to the dish and gently press it into the bottom and sides.

Spoon the seasoned apples into the crust, arranging them into a slightly rounded mound. If desired, dot with small pieces of butter.

Roll out the second pastry disk and place it over the apples. Trim excess dough, and crimp the edges to seal. Cut several small vents in the top crust.

Brush the crust with the egg wash and sprinkle with coarse sugar if desired. Bake in a preheated oven until the crust is deeply golden and the filling is bubbling through the vents.

Allow the pie to cool until the juices thicken before slicing.