Prepare the Pastry Dough
Mix the flour, sugar, and salt in a large bowl. Using your fingertips or a pastry cutter, work the cold butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces remaining.Combine the ice water and apple cider vinegar, then drizzle over the flour mixture, stirring with a fork until the dough just begins to come together. Don't overwork it!
Gather the dough, divide it into two discs, wrap in plastic, and refrigerate for at least 30 minutes.
Prepare the Apple Filling
Peel, core, and dice the apples into small, uniform cubes (about ¼-inch pieces).In a medium saucepan, combine the diced apples, brown sugar, lemon juice, cornstarch, cinnamon, nutmeg, allspice, and salt.
Cook over medium heat for about 5-7 minutes, stirring frequently until the apples are slightly softened but still maintain some texture. Remove from heat and let cool completely.
Assemble the Hand Pies
Preheat your oven to 375°F (190°C) and line two baking sheets with parchment paper.On a lightly floured surface, roll out one disc of dough to about ⅛-inch thickness. Using a 4-inch round cutter (or a bowl as a template), cut out circles from the dough.
Place about 1½ tablespoons of the cooled apple filling in the center of each circle, leaving a ½-inch border around the edges.
Brush the edges lightly with water to help seal the pies. Fold the dough over to create a half-moon shape and press the edges firmly to seal. For a decorative touch, crimp the edges with a fork.
Finish and Bake
Arrange the hand pies on the prepared baking sheets, spacing them about 2 inches apart. Using a sharp knife, cut a small slit or decorative vent in the top of each pie to allow steam to escape during baking.Whisk together the egg and 1 tablespoon of water to create an egg wash. Brush each pie with the egg wash and sprinkle with coarse sugar if desired.
Bake for 22-25 minutes, rotating the pans halfway through, until the pies are golden brown and the filling is bubbling. Allow to cool for at least 10 minutes before serving.