Preheat the oven to 425 degrees.
Prepare a large, rimmed baking sheet with parchment paper spritzed with nonstick cooking spray.
Roll out each sheet of puff pastry on a lightly floured surface.
Cut each sheet into 6 equal rectangles.
Place 2 asparagus on each rectangle diagonally.
Sprinkle the asparagus with salt and black pepper as desired. Top with a sprinkle of cheese.
Fold the opposite ends of the puff pastry over the asparagus.
Place on the prepared baking sheet.
Brush the puff pastry with the beaten egg.
Sprinkle with additional salt and black pepper if desired.
Bake for 12 to 15 minutes or until the puff pastry is golden.