Preheat the oven to 450 degrees F. Line a baking sheet or cookie sheet with parchment.
Mix the Parmesan and cayenne together until well combined.
Wrap each breadstick with a slice of prosciutto, then sprinkle with the Parmesan mixture.
Place the breadsticks on the prepared baking sheet and transfer to the oven. Bake for 5 minutes. Cool slightly and serve immediately.