Thaw shrimp, if frozen. Remove shells from shrimp, leaving tails. Butterfly each shrimp by cutting a slit along its back; remove vein. Rinse shrimp and pat dry with paper towels.
For stuffing, combine basil, Parmesan cheese, and garlic in small bowl. Place stuffing in slits. Leaving tail exposed, wrap each shrimp with half-slice of bacon, tucking in ends. Heat oven to 400 degrees F. Place shrimp on baking sheet with tails pointing up. Bake until shrimp turn opaque, about 14 minutes. Drain on paper towels. Dip shrimp into barbecue sauce and place on grill until sauce caramelizes or return to baking sheet and bake until sauce is caramelized, about 3 minutes.