Prepare the Pie Crust: In a large bowl, whisk together the flour and salt. Cut in the cold butter using a pastry blender or your fingers until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining. Gradually add ice water, 1 tablespoon at a time, mixing until the dough just comes together. Do not overmix.

Divide the dough in half, flatten each half into a disk, wrap tightly in plastic wrap, and chill in the refrigerator for at least 1 hour.

Prepare the Filling: In a large bowl, gently toss the sliced peaches with the granulated sugar, cornstarch, lemon juice, cinnamon, and nutmeg until evenly coated. Set aside while you roll out the bottom crust.

Assemble the Pie: Preheat your oven to 400°F (200°C). On a lightly floured surface, roll one disk of chilled dough into a 12-inch circle. Carefully transfer the dough to a standard 9-inch pie dish. Trim the edges, leaving about a 1-inch overhang. Pour the peach filling into the crust. Dot the top of the filling evenly with small pieces of butter.

Top and Crimp: Roll out the second disk of dough for the top crust. Place it over the filling (or cut into strips for a lattice top). Trim and crimp the edges of the top and bottom crusts together to seal. Cut a few slits in the top crust (if not using a lattice) to allow steam to escape.

Egg Wash and Bake: Whisk the egg and milk/water together to create an egg wash. Brush the top crust lightly with the wash and sprinkle generously with coarse sugar. Place the pie on a baking sheet (to catch drips). Bake at 400°F (200°C) for 15 minutes.

Reduce oven temperature to 375°F (190°C) and continue baking for another 45-50 minutes, or until the crust is golden brown and the filling is bubbling thickly. If the edges begin to brown too quickly, cover them loosely with foil.

Cool Completely: Let the pie cool on a wire rack for at least 3–4 hours before slicing and serving. This cooling time allows the filling to set properly.