For a charcoal grill, grill burgers on the rack of an uncovered grill directly over medium coals for 8 minutes, turning once halfway through grilling and brushing with vegetable broth several times. Add pineapple and onion slices to grill for the last 3 minutes of grilling time, turning once halfway through grilling. Add bun, split side down, to grill for the last 1 minute of grilling time. (For a gas grill, preheat grill. Reduce heat to medium. Place patties on grill rack over heat. Cover and grill as above.)
Serve burgers on grilled buns, topped with pineapple, onion, cheese, salad dressing, and lettuce. Makes 4 burgers.