Preheat the oven to 425°F (220°C). Line a baking sheet with parchment paper.
Roll the puff pastry out on a floured work surface, to form a large rectangle, double the original size. Square off edges and cut into 6 squares each.
Toss asparagus in olive oil and season with salt and pepper.
Fold a piece of prosciutto in half and set it on a puff pastry square. Add 3-4 stalks of asparagus, and a handful of cheese.
Bring the two opposite corners of the puff pastry squares to the middle and wrap them around the bundle. Press to seal. Brush with egg wash. Season with salt and pepper.
Bake until puff pastry is golden and crisp, about 10-13 minutes.