Pour the sugar and 1/2 cup of water into a small saucepot, trying to keep the sugar in the middle of the pot to avoid crystallization on the sides. Bring to a boil and cook until the syrup is thick and pecan brown, 15 to 20 minutes.
Add the heavy cream, be careful because it will bubble up. Stir in the butter and let cool completely, about 30 minutes.
Preheat the oven to 350 degrees F.
Punch out eight 4 1/2-inch circles from the pie dough. Toss the apples with 1/4 cup of the cooled caramel and the cinnamon. Brush the edges of the dough circles with beaten egg. Mound about 1 heaping tablespoon of the apple filling in the center of each circle. Fold the dough in half and crimp the edges with a fork.
Brush the tops with beaten egg and sprinkle with demerara sugar. Cut 2 small slits on top of each pie and bake on silicone-lined sheet pan until golden, 20 to 25 minutes. Drizzle the hand pies with leftover caramel sauce and serve.