In a food processor, combine gluten-free all-purpose flour, salt, and granulated sugar. Add the cold, cubed unsalted butter, processing until the mixture resembles coarse crumbs. Gradually pour in ice water, pulsing until the dough just comes together. Gather the dough into a ball, wrap it tightly in plastic wrap, and refrigerate for at least 30 minutes.

In a mixing bowl, combine the finely diced apples with light brown sugar, ground cinnamon, nutmeg, and gluten-free flour. Stir well until the apples are evenly coated, and set the mixture aside.

Preheat your oven to 425°F (220°C). Grease the muffin tin lightly with cooking spray or butter.

Remove your chilled dough and roll it out to about 1/8 to 1/4 inch thick. Cut out circles from the dough.

Press each dough circle into the wells of your prepared muffin tin. Spoon the apple filling into each crust, filling them generously. Brush the edges with an egg wash.

Bake the mini pies for 20 to 24 minutes, or until the crusts are golden brown and the filling is bubbling.

Allow the mini pies to cool in the tin for about 10 minutes, then transfer them to a wire rack to cool completely.