Whisk together flour and salt, then cut in cold butter until pea-sized pieces remain. Gradually add ice water, mixing until just combined; divide dough in half, flatten into discs, wrap, and refrigerate for at least 30 minutes.

Preheat oven to 400°F (200°C). Peel, core, and slice apples, then toss them with sugar, flour (or cornstarch), spices, and lemon juice until evenly coated.

On a floured surface, roll one chilled dough disc into a 12-inch circle and transfer it to a 9-inch pie plate. Trim edges, leaving a ½-inch overhang, then chill the pie plate.

Pour the apple mixture into the prepared pie crust, mounding it in the center, and dot the top with small pieces of butter.

Roll out the second dough disc into an 11-inch circle, which can be placed directly over the filling or cut into strips for a lattice top.

Place the top crust over the filling, trim, and crimp the edges of both crusts together to seal; if using a lattice, weave strips and then crimp edges, and cut a few slits in a solid top crust for steam release.

Whisk an egg with water for an egg wash, then brush it evenly over the top crust and sprinkle with coarse sugar.

Place pie on a baking sheet, bake at 400°F (200°C) for 20 minutes, then reduce to 375°F (190°C) and bake for 40-50 more minutes until golden and bubbly, tenting edges with foil if needed.

Allow the pie to cool on a wire rack for at least 3-4 hours before slicing to ensure the filling sets properly.