Heat the oven to 400°F. Line a large baking sheet with parchment paper.
Trim the woody ends from the asparagus, then pat the spears dry. If your spears are thick, slice them in half lengthwise.
Lay one prosciutto slice flat. Place 2 asparagus spears across one end and roll the prosciutto snugly around them. Set the bundle seam-side down on the baking sheet and repeat to make 12 bundles.
Drizzle the bundles with olive oil and sprinkle with black pepper.
Bake for 12-15 minutes, until the asparagus is crisp-tender and the prosciutto edges are lightly crisped.
Sprinkle the Parmesan over the bundles and bake 1-2 minutes more, just until it melts.
Serve warm with lemon wedges.