In a large bowl, whisk together the flour, salt, and sugar until well combined. Add the cold, cubed unsalted butter, and use a pastry cutter or your fingertips to mix until the mixture resembles coarse crumbs. Gradually stir in the cold water until the dough starts to come together.

Once the dough is formed, divide it into two equal discs and wrap each in plastic wrap. Refrigerate the discs for at least 30 minutes.

While the dough chills, prepare the apple filling. In a medium bowl, combine the diced apples, sugar, cinnamon, nutmeg, lemon juice, and flour. Toss gently until all the apples are evenly coated.

Set your oven to preheat at 375°F (190°C).

On a lightly floured surface, take one of the chilled dough discs and roll it out to about ⅛ inch thick. Using a round cutter, cut out circles that fit each muffin cup in your greased muffin tin.

Carefully place each dough circle into the muffin tin cups, ensuring they sit snugly against the sides. Fill each with a generous spoonful of the prepared apple mixture.

Roll out the second disc of dough and cut out smaller circles or fun shapes for the tops of your pies. Place each top over the filled cups and pinch the edges to seal them well.

Gently brush the tops of each mini pie with the beaten egg.

Place the muffin tin in the preheated oven and bake for about 20-25 minutes.

Once baked, remove the Mini Apple Pies from the oven and allow them to cool for a few minutes.