Prepare the Dough: In a large bowl, whisk together flour, salt, and sugar. 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.

Chill the Dough: Divide the dough in half, form each half into a flat disk, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes.

Make the Filling: In a medium bowl, gently toss the diced nectarines with brown sugar, cornstarch, cinnamon, nutmeg, and lemon juice. Set aside while you roll out the dough.

Assemble Pies: Preheat oven to 400°F (200°C). On a lightly floured surface, roll out one disk of dough to about 1/8-inch thickness. Use a 5-inch round cutter (or bowl rim) to cut out circles. Repeat with the second disk of dough. Place half the dough circles on a parchment-lined baking sheet.

Fill and Seal: Spoon about 1 to 1.5 tablespoons of the nectarine filling onto the center of each round, leaving a 1/2-inch border. Brush the edges lightly with water. Place the second dough circle over the filling and crimp the edges firmly with a fork to seal. Cut two small slits on the top of each pie to allow steam to escape.

Bake the Pies: Whisk the egg with milk or water to create the egg wash. Brush the tops of the pies with the wash and sprinkle generously with coarse sugar. Bake for 20-25 minutes, or until the crust is golden brown and the filling is bubbling.

Cool and Serve: Let the hand pies cool on the baking sheet for 10 minutes before transferring them to a wire rack to cool slightly further. Serve warm or at room temperature.