Separate breadstick dough into 12 pieces; cut each piece in half lengthwise to form 2 thin strips. Wrap prosciutto around 12 dough strips. Twist unwrapped dough strips around prosciutto-wrapped pieces; twist 3 or 4 times, pinching ends to seal. Coat twists with cooking spray.
Combine cheese and rosemary in a pie plate or shallow dish; roll breadsticks in cheese mixture.
Place breadsticks on a baking sheet coated with cooking spray.
