Prepare the apples: Peel, core, and finely dice the apples into small, even pieces.
Cook the filling: Melt the butter in a skillet over medium heat. Add the diced apples, sugar, cinnamon, vanilla extract, lemon juice, and optional nutmeg.
Soften the apples: Cook for about 5–7 minutes, stirring occasionally, until the apples are tender but still hold their shape. Remove from the heat and allow the filling to cool slightly.
Prepare the pastry: Place the thawed puff pastry on a lightly floured surface and gently roll it out if needed. Cut it into 12 small squares.
Add the filling: Place a small spoonful of the apple mixture in the center of each pastry square. Avoid overfilling.
Seal the bites: Fold the pastry over the filling and press the edges together firmly. Use a fork to crimp and seal the edges.
Prepare for baking: Arrange the apple pie bites on a parchment-lined baking sheet.
Add egg wash: Beat the egg with 1 tablespoon of water. Lightly brush the tops of the pastry with the egg wash. Sprinkle with cinnamon sugar if desired.
Bake: Bake in a preheated 375°F (190°C) oven for 18–22 minutes, or until the pastry is puffed and golden brown.
Cool and serve: Remove from the oven and allow the apple pie bites to cool for a few minutes before serving.