Keeping the cheese cold--one reader even suggested freezing--until you are ready to assemble and grill will allow the prosciutto to become crisp before the cheese melts too much. You may also prep these in advance, cover, and refrigerate until you are ready to grill. Very thinly sliced prosciutto will become crisp quickly before the cheese has time to ooze out.
Sargento String Cheese, very cold (could also use Provolone Mozzarella or variety of choice)
Prosciutto, very thinly sliced (2 pieces for every 1 string cheese)
Optional: fresh basil, slivered
Instructions
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!
Notes
I find it easiest to work with prosciutto within the first couple days of purchasing. Because the slices are so delicate, they tend to stick to one another and tear more easily after they have sat in the fridge for a few days. Fresh pieces of prosciutto will separate easily and, thus, be less likely to tear. In turn, the cheese will not be as likely to ooze out.