Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.
Core the apples and slice into rings about ¼-inch thick.
Roll out the puff pastry and cut into strips.
Mix the brown sugar, cinnamon, and nutmeg (if using) in a small bowl.
Wrap each apple ring with a puff pastry strip, brushing with egg wash and sprinkling with the cinnamon-sugar mixture as you go.
Place on the baking sheet and bake for 18-20 minutes, until the pastry is golden and puffed.
Serve warm with powdered sugar or caramel sauce, if desired.