In a mixing bowl, combine the flour and salt. Cut in the butter until the mixture resembles coarse crumbs.

Add the ice water, one tablespoon at a time, mixing until the dough comes together. Shape the dough into a disc and wrap it in plastic wrap. Refrigerate for at least 1 hour.

Preheat the oven to 425°F (220°C).

In a large bowl, combine the sliced apples, sugar, cinnamon, nutmeg, lemon juice, and cornstarch. Mix well.

Roll out half of the pie dough on a lightly floured surface to fit a 9-inch pie pan. Transfer the dough to the pan.

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

Roll out the remaining pie dough and place it over the filling. Trim and seal the edges. Cut slits in the top crust to allow steam to escape.

Brush the top crust with milk and sprinkle with sugar.

Bake for 40-45 minutes, or until the crust is golden brown and the filling is bubbly.

Allow the pie to cool before serving.