Place 1 basil leaf at the short end of a slice of prosciutto and a shrimp on top of the basil. Roll the shrimp in the prosciutto, then thread lengthwise onto a skewer. Repeat with the remaining basil, prosciutto, and shrimp. Place the skewers on a baking sheet and refrigerate until ready to cook.

To make the sauce, combine the vinegar, mustard and garlic in a food processor or blender. With the machine running, add the olive oil in a slow, steady stream. Process until combined. 10-15 minutes before you are ready to grill, spoon about 1/3 of the sauce over the shrimp skewers to marinate. Transfer the rest of the dipping sauce to a small bowl. Prepare a medium-hot fire in a grill. Grill the shrimp, turning often, until opaque, about 6 minutes. Arrange the cooked skewers on a platter and serve with the dipping sauce on the side.