In a large bowl, whisk together flour, salt, and sugar. Add the cold cubed butter and use a pastry cutter or your fingertips to work it in until the mixture resembles coarse crumbs with some pea-sized pieces remaining.
Mix 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. If the dough seems too dry, add additional ice water, 1 tablespoon at a time.
Form the dough into a disk, wrap tightly in plastic wrap, and refrigerate for at least 30 minutes or up to 2 days.
In a large skillet over medium heat, combine diced apples, brown sugar, lemon juice, and butter. Cook for 5-7 minutes until apples begin to soften but still hold their shape. Stir in cinnamon, nutmeg, and cloves.
Mix cornstarch and water in a small bowl to create a slurry, then add to the apple mixture. Cook for another 1-2 minutes until the filling thickens. Remove from heat and let cool completely.
Preheat your oven to 375°F (190°C) and line two baking sheets with parchment paper.
Roll out the chilled dough on a lightly floured surface to about ⅛-inch thickness. Using a 4-inch round cutter or a bowl as a guide, cut out circles from the dough.
Place about 1½ tablespoons of the cooled apple filling in the center of each dough circle, leaving a ½-inch border around the edges.
Fold the dough over to create a half-moon shape. Press edges firmly to seal, then use a fork to crimp the edges decoratively or fold and twist the edges to create a rope-like pattern.
In a small bowl, beat the egg with 2 tablespoons of water to create an egg wash. Brush the tops of the empanadas with the egg wash, then sprinkle with coarse sugar. If desired, mix cinnamon with the sugar for extra flavor.
Using a sharp knife, cut a small vent in the top of each empanada to allow steam to escape during baking.
Bake for 20-25 minutes, or until the empanadas are golden brown and the filling is bubbling. Rotate pans halfway through baking for even browning.