Prepare the Apple Filling: In a medium saucepan, melt the butter over medium heat. Add the diced apples and cook for 5-7 minutes, stirring occasionally, until the apples soften. Stir in the brown sugar, cinnamon, nutmeg (if using), lemon juice, and vanilla extract. Cook for an additional 3-4 minutes until the mixture thickens slightly. Remove from heat and let it cool.

1. Preheat the Oven: Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper.
2. Prepare the Puff Pastry: Unroll the thawed puff pastry sheet on a lightly floured surface. Cut the pastry into small squares or rectangles, about 3×3 inches or to your preferred size.
3. Assemble the Bites: Place a small spoonful of the apple filling in the center of each puff pastry square. Fold the corners over the filling to form a parcel or triangle shape (or leave them open). Pinch the edges to seal them.
4. Egg Wash: Beat the egg and brush it over the top of each pastry bite to give them a golden finish when baked.
5. Sprinkle with Sugar: Sprinkle a little sugar over the top for extra sweetness and a nice crunch.
6. Bake: Place the mini pies on the prepared baking sheet and bake for 15-20 minutes, or until the puff pastry is golden brown and flaky.
7. Serve: Let the bites cool slightly before serving. Serve warm and enjoy!