Prepare the Crust: In a large bowl, whisk together the flour, 1 teaspoon sugar, and salt. Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs with some pea-sized pieces of butter remaining.

Gradually add the ice water, one tablespoon at a time, mixing until the dough just comes together. Do not overmix. Form the dough into a disk, wrap tightly in plastic wrap, and chill in the refrigerator for at least 30 minutes.

Prepare the Filling: In a separate large bowl, gently toss the peach slices with the 1/2 cup sugar, cornstarch, lemon juice, cinnamon, and nutmeg until thoroughly coated. Set aside while you roll out the dough.

Assemble the Galette: Preheat your oven to 400°F (200°C). On a lightly floured surface, roll the chilled dough out into a rough 14-inch circle. Carefully transfer the dough circle onto a baking sheet lined with parchment paper.

Arrange the peaches in the center of the dough, leaving a 2-inch border all around. Gently fold the edges of the dough up and over the fruit, overlapping slightly to create a rustic edge. Brush the exposed crust with the beaten egg wash and sprinkle generously with coarse sugar.

Bake for 40 to 50 minutes, or until the crust is golden brown and the fruit juices are bubbling thickly. If the edges brown too quickly, loosely cover them with small strips of aluminum foil.

Let the galette cool on the baking sheet for at least 15 minutes before slicing and serving warm. Excellent served with vanilla bean ice cream.