In a large bowl, combine flour and salt. Cut in the cold butter until the mixture resembles coarse crumbs. Gradually add ice water until the dough forms. Divide the dough and chill for at least 1 hour.

Toss the sliced apples with lemon juice, both sugars, flour, cinnamon, nutmeg, and a pinch of salt. Let the mixture sit for 20 minutes to develop those delicious flavors.

Roll out one chilled dough disc into a 12-inch circle. Carefully fit it into a 9-inch pie dish. Roll the second disc to create your top crust or a lovely lattice.

Fill the pie shell with the apple mixture, and dot the top with butter for extra richness. Cover with the top crust, crimp the edges, and cut vents or weave a lattice for that classic touch.

Brush the top with the beaten egg and milk mixture for a gorgeous golden finish. If you like, sprinkle coarse sugar over the top for added sweetness and crunch.

Bake at 400°F (200°C) for 20 minutes, then reduce the temperature to 375°F (190°C) and bake for another 35-40 minutes, until the crust is golden brown and the filling is bubbling.

Let the pie cool on a wire rack for at least 2 hours before slicing.