Unwrap the cheese, and cut each stick in half so you have two short pieces.
Wrap one piece of prosciutto around each cheese half, being careful to completely cover all the cheese, including the ends. If you have small pieces of prosciutto that break off, use those to shore up the ends. The prosciutto is “sticky” enough that you should not have to secure with a toothpick. If desired, you may place a small amount of the slivered basil between the cheese and the prosciutto.
Grill over medium heat, turning frequently, until the outsides become slightly crisp and the cheese becomes gooey. This will only take a couple of minutes.
Remove to a platter, cool slightly, and enjoy!