Make the Pie Crust:

In a large bowl, combine flour, salt, and sugar. Add the chilled butter pieces and, using a pastry cutter or your fingers, cut the butter into the flour until the mixture resembles coarse crumbs.

Gradually add ice water, 1 tablespoon at a time, mixing with a fork until the dough starts to come together. You may not need all the water.

Turn the dough out onto a floured surface and knead briefly to bring together. Divide the dough in half, shape into disks, wrap in plastic wrap, and refrigerate for at least 1 hour.

Prepare the Filling:

In a large bowl, combine the sliced apples, sugar, flour, melted butter, cinnamon, nutmeg, and lemon juice. Toss to coat the apples evenly. Set aside.

Assemble the Pie:

Preheat your oven to 375°F (190°C).

On a floured surface, roll out one disk of dough into a 12-inch circle. Transfer it to a 9-inch pie dish. Trim the edges, leaving a slight overhang.

Fill the crust with the apple mixture, mounding it slightly in the center.

Roll out the second disk of dough and place it over the filling. Trim the overhang to about 1 inch, then fold the top crust under the bottom crust edge, pressing to seal. Cut slits in the top to vent.

Brush the crust with the egg wash and sprinkle with coarse sugar if using.

Bake the Pie:

Bake in the preheated oven for about 50 minutes, or until the crust is golden brown and the filling is bubbly.

If the edges of the pie start to brown too quickly, cover them with foil or a pie shield.

Cool and Serve:

Allow the pie to cool on a wire rack for at least 2 hours before serving. This resting time helps the filling set up, making the pie easier to slice.