Preheat oven to 375°F. Grease a large rimmed baking sheet with nonstick cooking spray and set aside. In a medium bowl, combine shrimp, 1 tablespoon olive oil, 1 tablespoon minced garlic and tarragon then season to taste with salt, pepper and granulated garlic. Carefully toss ingredients to coat well. Wrap each shrimp with half slice of prosciutto, secure with toothpick and place on a prepared baking sheet, about 1 inch apart. Set aside. In a small sauce pot, heat remaining olive oil over medium-high heat. Add red onions, remaining minced garlic and rosemary then sauté 2–3 minutes or until vegetables are wilted. Add cane syrup, brown sugar, Creole mustard and apple juice, whisking to blend thoroughly. Add barbecue sauce, Worcestershire sauce, hot sauce and rum. Season lightly using salt, pepper and granulated garlic. Bring to a low simmer and cook 5–7 minutes or until heated thoroughly, stirring constantly. Using a pastry brush, paint shrimp with barbecue sauce and bake 5 minutes. Turn shrimp once, paint with more barbecue sauce and cook an additional 5 minutes or until pink and curled. Do not overcook. Serve with lemon wedges and remaining barbecue sauce for dipping.