Step 1: In a large bowl, combine the diced apples, brown sugar, flour, cinnamon, nutmeg, and lemon juice. Stir gently until the apples are evenly coated.
Step 2: On a lightly floured surface, unroll one pie crust. Using a 4-inch round cutter or a large glass, cut out as many circles as possible. Repeat with remaining pie crusts, gathering and re-rolling scraps as needed. You should get about 8-10 circles total.
Step 3: Place a tablespoon of the apple filling onto one half of each pie crust circle. Drizzle about 1 teaspoon of caramel sauce over the apple filling.
Step 4: Fold the other half of the pie crust over the filling to create a half-moon shape. Press the edges together firmly with your fingers, then use the tines of a fork to crimp and seal the edges completely. Cut 2-3 small slits on the top of each hand pie to allow steam to escape.
Step 5: Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper. Arrange the hand pies on the prepared baking sheet. Brush the tops of each pie with the beaten egg wash and sprinkle with coarse sugar.
Step 6: Bake for 20-25 minutes, or until the crust is golden brown and the filling is bubbling. Let cool slightly on a wire rack before serving.