1. Melt butter in a skillet over medium heat. Add diced apples, brown sugar, cinnamon, nutmeg, vanilla extract, and lemon juice. Cook for 5–7 minutes until apples soften. Stir in cornstarch if a thicker filling is desired, then cool completely.

2. In a bowl, combine cream cheese, sugar, and vanilla extract. Beat until smooth and creamy. Chill if needed.

3. Preheat oven to 400°F (200°C). Unfold puff pastry on a floured surface and cut each sheet into 4 squares.

4. Add a tablespoon of cheesecake filling and apple mixture to each square. Fold over, forming a triangle or rectangle. Crimp edges with a fork to seal.

5. Place pies on a parchment-lined baking sheet. Mix egg with milk or water and brush tops with the wash.

6. Bake for 18–22 minutes until puffed and golden.

7. Cool on a wire rack and dust with powdered sugar before serving.