Preheat the oven to 400°F (200°C). Line two baking sheets with parchment paper and set aside.

In a medium skillet over medium heat, melt the butter. In a separate small bowl, whisk together the brown sugar, cornstarch, cinnamon, and nutmeg. Add the dry mixture and chopped apples to the skillet. Stir to coat the apples thoroughly. Cover the skillet and allow the mixture to simmer for approximately 5 minutes, or until the apples begin to soften slightly. Remove from heat and let the filling cool for at least 10 minutes.

On a lightly floured surface, roll out the pie crusts to approximately 1/8-inch thickness. Using a 3.5-inch round cookie cutter or similarly sized object, cut out circles from the dough. Reroll the scraps and continue cutting until all the dough is used. Place the dough rounds on the prepared baking sheets.

Spoon a small amount of the cooled apple filling onto half of the dough circles, leaving a slight border around the edges. Moisten the edges of each circle with a small amount of water, then place a second dough circle on top. Press the edges together gently and seal by crimping with the tines of a fork.

In a small bowl, whisk together the beaten egg and milk. Brush the top of each assembled hand pie with the egg wash mixture. Sprinkle each with coarse sugar. Using a sharp knife, cut three small slits in the top of each pie to allow steam to escape during baking.

Place the baking sheets in the preheated oven and bake for 18 to 22 minutes, or until the hand pies are golden brown and crisp. Remove from the oven and allow to cool on a wire rack for several minutes before serving.