Heat the oven to 425 degrees.
Roll the puff pastry sheets out onto a lightly floured surface,and cut each one into 6 evenly sized squares.
Add the asparagus to a mixing bowl, and drizzle with the olive oil.
Sprinkle the asparagus with the thyme and salt and pepper to taste.
Place a piece of prosciutto into the center of each piece of puff pastry.
Top with 3-4 spears of asparagus and 2 Tbsp of the cheese.
Fold opposite ends of each square up to cover the asparagus fulling, and pinch closed to seal.
Brush the tops of the bundles with the beaten egg.
Place the bundles onto a parchment lined baking sheet, and bake for 12-15 minutes.