Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.

Prepare the apple filling:

In a small skillet over medium heat, melt the butter. Add the diced apples, granulated sugar, brown sugar, cinnamon, and nutmeg (if using). Stir and cook for about 5–7 minutes, until the apples are slightly tender but not mushy.

Thicken the filling:

In a small bowl, mix the cornstarch and water together to form a slurry. Pour it into the apple mixture and stir for 1–2 minutes until the filling thickens. Remove from heat and let cool slightly.

Flatten the biscuits:

Separate the biscuit dough and place each round on a lightly floured surface or piece of parchment. Use your fingers or a rolling pin to gently flatten each biscuit into a 4–5 inch circle.

Fill and fold the turnovers:

Place a heaping tablespoon of the cooled apple filling in the center of each biscuit round. Fold the dough over to create a half-moon shape and press the edges to seal. Use the tines of a fork to crimp the edges tightly.

Apply the egg wash:

In a small bowl, whisk the egg and milk together. Brush the tops of each turnover with the egg wash for a glossy golden finish.

Bake the turnovers:

Arrange the turnovers on the prepared baking sheet, spaced evenly. Bake for 15–18 minutes, or until golden brown and puffed.

Cool and top:

Allow the turnovers to cool for at least 5 minutes before serving. Dust with powdered sugar or drizzle with a simple glaze if desired.