Prepare the puff pastry: Preheat oven to 400°F (200°C). Roll out the thawed puff pastry sheets and cut into equal rectangles. Place on a baking sheet lined with parchment, prick with a fork, and bake for 12–15 minutes or until golden and crisp. Let cool completely.

1. Make the caramelized apples: In a skillet, melt butter over medium heat. Add apple slices, brown sugar, and cinnamon. Cook, stirring occasionally, until apples are tender and caramelized (about 8–10 minutes). Let cool.
2. Prepare the pastry cream: In a medium saucepan, whisk together milk, sugar, cornstarch, salt, and egg yolks. Cook over medium heat, whisking constantly, until thickened (5–7 minutes). Remove from heat, stir in vanilla, and let cool completely.
3. Assemble: Layer one piece of baked puff pastry with pastry cream, then a layer of caramelized apples. Repeat for 2–3 layers, finishing with a top layer of pastry.
4. Chill and serve: Refrigerate for at least 1 hour to set. Dust with powdered sugar or drizzle with a light icing before serving. Slice carefully with a serrated knife.