Whisk together flour and salt in a large bowl.

Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs. Work quickly to keep the butter cold.

Gradually add ice water, a tablespoon at a time, mixing lightly until the dough just comes together. Don't overmix.

Form the dough into a disc, wrap in plastic wrap, and chill for at least 30 minutes.

In a large bowl, combine the sliced apples, granulated sugar, brown sugar, flour, cinnamon, nutmeg, salt, and lemon juice. Toss gently to coat.

Preheat oven to 375°F (190°C).

On a lightly floured surface, roll out half of the chilled dough into a 12-inch circle. Carefully transfer to a 9-inch pie plate.

Pour the apple filling into the pie crust. Dot with the small pieces of butter. Roll out the remaining dough and either place it over the filling or cut it into strips for a lattice top. Crimp the edges to seal. Cut slits in the top crust to allow steam to escape.

Bake for 45-55 minutes, or until the crust is golden brown and the filling is bubbly. If the crust starts to brown too quickly, cover the edges with aluminum foil.

Let cool completely on a wire rack before serving.