Drain pineapple, reserving 2 tablespoons syrup for sauce.
Season meat with salt and pepper.
Press a scant tablespoon of meat into center of each pineapple slice, overlapping meat on pineapple around center on both sides of slice so meat won't fall out while cooking.
Shape remaining meat in 4 patties, slightly larger in diameter than the pineapple; broil burgers on grill over hot coals 12 to 15 minutes, turning once.
Broil meat-filled pineapple slices, turning carefully and brushing with Island Sauce till meat is done and pineapple glazed.
To assemble, place each burger atop a bun half or slice of toast.
Top with pineapple burger.
Peg with a kabob of cherry tomato and green olive.
Island Sauce: Mix reserved pineapple syrup, 1/2 cup catsup, 1/4 cup brown sugar, 2 teaspoons Worcestershire sauce, and a few drops liquid smoke; heat to boiling.