Make the Pie Crust:

1. In a large bowl, whisk together flour, sugar, and salt. Add the cold butter cubes and use a pastry cutter or fork to cut the butter into the flour until the mixture resembles coarse crumbs with some pea-sized butter pieces remaining.
2. Add ice water one tablespoon at a time, mixing gently with a fork after each addition. Add just enough water for the dough to come together when pressed. It should be slightly shaggy but hold together.
3. Divide the dough in half, shape each half into a flat disk, and wrap tightly in plastic wrap. Refrigerate for at least 1 hour or up to 2 days.

Prepare the Apple Filling:

4. Peel, core, and slice the apples into ¼-inch thick slices. Place them in a large bowl.
5. Add granulated sugar, brown sugar, flour (or cornstarch), cinnamon, nutmeg, salt, and lemon juice to the apples. Toss everything together until the apples are evenly coated. Let the mixture sit for 15-20 minutes to allow the flavors to meld and the apples to release some juice.

Assemble the Pie:

6. Preheat your oven to 400°F (200°C). Place a baking sheet on the lower rack to catch any drips.
7. On a lightly floured surface, roll out one disk of dough into a 12-inch circle, about ⅛-inch thick. Carefully transfer it to a 9-inch pie dish, letting the excess hang over the edges. Gently press the dough into the bottom and sides of the dish.
8. Pour the apple filling into the crust, mounding it slightly in the center. Dot the filling with the 2 tablespoons of butter pieces.
9. Roll out the second disk of dough into a 12-inch circle. Place it over the filling. Trim the excess dough to about 1 inch beyond the edge of the pie dish. Fold the top crust edge under the bottom crust edge and crimp or flute the edges to seal.
10. Cut 4-5 slits in the top crust to allow steam to escape. You can also create decorative shapes if desired.
11. Brush the top crust with egg wash and sprinkle with coarse sugar if using.

Bake the Pie:

12. Place the pie on the preheated baking sheet in the oven. Bake at 400°F for 20 minutes.
13. Reduce the temperature to 375°F (190°C) and continue baking for 40-50 minutes, until the crust is deep golden brown and the filling is bubbling through the vents.
14. If the edges are browning too quickly, cover them with a pie shield or strips of aluminum foil.
15. Remove from the oven and let the pie cool on a wire rack for at least 4 hours before slicing. This cooling time allows the filling to set properly.