Mix turkey and 2 tablespoons of the Bar-B-Q Sauce in medium bowl until well blended. Shape into 4 burger patties. Brush onion slices with oil.
Grill burgers over medium heat 4 to 6 minutes per side or until cooked through (internal temperature reaches 165°F). Grill onions alongside burgers until slightly charred.
Serve burgers on rolls, topped with remaining Bar-B-Q Sauce, grilled onion and avocado.