Preheat your grill to medium-high heat (around 400°F).
In a small bowl, mix the diced mango, pineapple, avocado, and cilantro to create the fruit salsa. Set aside in the refrigerator.
Form the ground beef into four equal 4-ounce patties. Season both sides with half of the salt and black pepper.
Toss the zucchini and bell peppers in a bowl with a light coating of oil and the remaining seasoning.
Place the beef patties and vegetables on the grill. Cook the burgers for 4 to 5 minutes per side, brushing with BBQ sauce during the last 2 minutes. Grill vegetables until tender and lightly charred, about 5-7 minutes.
While the beef cooks, toss the shrimp with melted butter, lemon juice, rosemary, and parsley. Sear the shrimp on a grill pan or directly on the grates for 2 minutes per side until pink and opaque.
Lightly toast the hamburger buns on the grill for 30 seconds.
Assemble the burgers with buns, lettuce, red onion, and the BBQ beef patties. Serve alongside the herb shrimp, grilled vegetables, and fresh fruit salsa.