Prepare the shrimp: Mix the basil, cheese and garlic in a bowl. Slice down the back of each shrimp and remove the vein; fill the cut with 1/2 teaspoon of the basil mixture. Wrap each shrimp with 1/2 slice bacon and secure with a toothpick, or tuck the loose end of the bacon under.
Build a fire (wood or charcoal and wood) for indirect cooking by situating the coals on one side of the grill. When the temperature reaches 400 degrees F, place the shrimp on the grill away from the coals. Close the lid and cook until the bacon is crisp and the shrimp is cooked through, about 14 minutes. Drain on a paper-towel-lined platter.
Mix all the sauce ingredients in a bowl. Dip each shrimp in the sauce and return to the grill away from the coals. Close the lid and allow the sauce to caramelize, about 3 minutes. Serve hot.
Photograph By Mark Peterson
Recipe courtesy Chris Lilly for Food Network Magazine