In a medium mixing bowl, combine the diced apples, brown sugar, cinnamon, nutmeg, lemon juice, and cornstarch. Mix until the apples are evenly coated. Let the mixture sit for a few minutes to allow the flavors to meld together and the cornstarch to start thickening the juices.

Lightly flour your work surface and unfold the thawed puff pastry sheet. Roll it out slightly to even it out. Cut the sheet into four equal squares.

Spoon an equal amount of the apple mixture onto one half of each pastry square, leaving a small border around the edges. Fold the pastry over the filling to form a triangle. Press the edges together to seal, then crimp the edges with a fork to ensure they are well sealed.

Lightly beat the egg in a small bowl. Brush the top of each turnover with the egg wash. For added sweetness and texture, sprinkle the tops with a little granulated sugar.

Preheat the air fryer to 350°F (175°C) if your model requires preheating. Place the turnovers in the air fryer basket, ensuring they are not touching. Depending on the size of your air fryer, you may need to cook them in batches.

Cook for about 15-20 minutes, or until the turnovers are golden brown and puffed up. Halfway through the cooking time, you may gently flip the turnovers to ensure even browning, but this is optional based on how your air fryer circulates air.

Carefully remove the turnovers from the air fryer and let them cool for a few minutes on a wire rack before serving. They're best enjoyed warm, offering a crispy outside with a juicy, flavorful apple filling.