Prepare the dough: In a large bowl, whisk together the flour, 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, 1 tablespoon at a time, mixing until the dough just comes together. Form the dough into a disk, wrap tightly in plastic wrap, and chill in the refrigerator for at least 30 minutes.

Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper. On a lightly floured surface, roll the chilled dough into a rough 14-inch circle. Transfer the dough carefully to the prepared baking sheet.

Prepare the filling: In a medium bowl, gently toss the sliced nectarines with the granulated sugar, cornstarch, lemon juice, and vanilla extract until evenly coated. Do not mix too vigorously to avoid crushing the fruit.

Assemble the galette: Arrange the nectarine slices 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, pleating as you go to form a rustic crust.

Brush the folded crust generously with the beaten egg wash and sprinkle the exposed fruit and crust edges with the coarse sugar.

Bake for 35 to 45 minutes, or until the crust is deep golden brown and the nectarine juices are bubbling thickly. If the edges brown too quickly, loosely cover them with foil.

Let cool on the baking sheet for at least 15 minutes before slicing and serving. Delicious served warm with vanilla ice cream or whipped cream.