Prepare the pie crust recipe. Chill in the fridge for at least 2 hours.
Melt the butter in a saucepan over medium-low heat. Add the diced apples, granulated sugar, cinnamon, nutmeg, lemon juice, and a pinch of salt and cook until the apples are tender, stirring occasionally, about 8-10 minutes. Add the flour, stir, and cook for 30 seconds or until the filling thickens. Transfer the filling to a bowl and allow it to cool completely. See notes.
Take the pie dough out of the fridge and let it sit at room temperature for 15-20 minutes to soften slightly. This will make it easier to roll out.
Lightly dust your surface with flour. Lay out the pie dough and use a rolling pin to roll it out to ⅛" inch thick. Transfer the rolled-out dough onto a parchment-lined baking sheet and stick it in the fridge to chill for about 10 minutes. The colder the dough, the easier it is to work with.
Use a 3.5" inch cookie cutter to cut out 12 circles. Roll out the scraps to cut out more circles if necessary. Place the cut circles onto the parchment-lined baking sheet and place it in the refrigerator to chill the dough so that it is firm.
Preheat the oven to 400°F and make sure the oven rack is in the center position.
Arrange 6 circles about 3 inches apart on the baking sheet; these are the bottom crusts. Fill the center of each circle with two tablespoons of the cooled apple pie filling, leaving a small border around the edge. Beat the egg and brush the border of each filled circle with the egg wash.
Using a sharp knife, cut three slits into the remaining 6 circles; these are the top crusts. The slits act as vents so that steam can escape as the pies bake.
Place the vented circles on the filled circles and gently press down on the edges to seal the pies shut. Then, crimp the edges with a fork and brush the surface of each pie with the egg wash.
In a small bowl, mix together the cinnamon and sugar. Generously sprinkle the top of each pie with the cinnamon-sugar mixture.
Bake for 15-20 minutes on the center rack. Allow the pies to cool on the baking sheet for 5 minutes, then transfer to a cooling rack.