PREPARE: Let the pie crust come to room temperature. Preheat the oven to 375˚ Fahrenheit and adjust the rack to the center position. Line a large cookie sheet with parchment paper and set aside.
MELT THE SUGAR: Heat a small sauce pan over medium and add the sugar. Let the sugar heat up for about 1-2 minutes, then begin folding the sugar that has melted on the bottom to the top. When the sugar starts to clump up, stir constantly until it has completely melted. This should take about 5-7 minutes.
FINISH THE CARAMEL SAUCE: Reduce the heat to low and slowly drizzle the melted butter into the sugar while continuing to stir. If the butter separates from the sugar, whisk quickly to incorporate. Next slowly pour in the warm half and half and bring to a low simmer. Simmer for 1-2 minutes until the sauce has thickened then remove from heat.
SEASON THE APPLES: In a medium bowl, toss together the apple, lemon juice, cinnamon, and nutmeg and set aside.
CUT OUT THE CRUSTS: On a lightly floured surface, roll out the pie crust and use a 3-inch biscuit cutter (or cut around a bowl or glass) to cut out circles in the pie crust. You should be able to get 8-10 out of one pie crust.
ASSEMBLE PIES: Drizzle ½ teaspoon of caramel sauce on one side of the pie crust circles. Top that with 2-3 apple slices, then another ¼ teaspoon of caramel sauce. Run a bead of beaten egg on the perimeter of the crust with your finger or a brush.
SEAL THE HAND PIES: Fold the crust in half, over the apples and sauce. Use a fork to press the hand pie closed. Arrange the pies on the prepared pan. Brush the the top of the pies with the beaten egg and sprinkle with the raw sugar. Pierce the pies 3 times in the center with a knife.
BAKE: Bake the pies for 18-20 minutes or until the crust is golden brown and firm. Allow them to cool for 10-15 minutes until serving. Serve with the remaining caramel sauce.
Do not forget to warm the half and half or melt the butter, the cooler temperature can solidify the melted sugar and ruin your caramel sauce.