In a large bowl, combine the sliced apples, brown sugar, flour, lemon juice, cinnamon sugar, and nutmeg. Mix well and refrigerate for 15-20 minutes.

Preheat the oven to 400°F (200°C). Rub a little butter on the bottom of a skillet or baking sheet to prevent sticking. Gently lay out the puff pastry on the skillet, letting the sides hang over. Press the dough lightly along the edges on the inside, leaving the edges overhanging.

Sprinkle a little extra cinnamon sugar and nutmeg on the bottom of the puff pastry. Spread the apple mixture evenly in the center of the pastry.

Fold the edges of the pastry over the apples. Brush the folded edges with the whisked egg and sprinkle with sugar for a golden finish.

Place in the preheated oven and bake for 35-45 minutes, until the crust is golden brown and the apples are tender.

Let cool slightly, then top with vanilla ice cream and a drizzle of caramel, if desired. Enjoy!