In a large bowl, whisk together the flour, sugar, and salt.
Cut the cold butter into the flour mixture using a pastry cutter or your fingers until it resembles coarse crumbs.
Gradually add ice water, one tablespoon at a time, mixing until the dough just comes together into a cohesive disk.
Wrap the dough in plastic and chill in the refrigerator for at least 30 minutes.
Prepare the filling by combining the diced apples, brown sugar, cinnamon, nutmeg, and lemon juice in a saucepan over medium heat, cooking until apples are slightly tender (about 5-8 minutes), then let cool completely.
Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
Roll out the chilled dough on a floured surface and cut into rounds using a 4-inch cookie cutter.
Place a spoonful of the apple mixture in the center of each round, fold the dough over to create a half-moon, and crimp the edges tightly with a fork.
Brush the tops with the egg wash and cut tiny steam vents on each pie.
Bake for 20-25 minutes until the pastry is golden brown.
Cool on a wire rack before serving.