Preheat oven to 400°F (200°C) and line a baking sheet with parchment paper.
Roll out puff pastry slightly and cut into 10–12 even strips.
Toss asparagus lightly with olive oil and black pepper.
Wrap one slice of prosciutto around each asparagus spear.
Place wrapped asparagus on a pastry strip and roll snugly.
Arrange bundles seam-side down on the baking sheet.
Brush pastry with egg wash and sprinkle with Parmesan if using.
Bake for 18–22 minutes until puffed and golden brown.
Cool for a few minutes before serving.