Form the ground beef into 4 patties, each about 3 1/2 inches across and 3/4-inch thick. Make a slight depression in the center. (Burgers rise more in the center than on the periphery, so the slight indentation helps give you an even thickness.) Generously season the burgers on both sides with the Kansas City Sweet and Smoky Rub and let marinate in the refrigerator while you light your grill.
Set up the grill for direct grilling and preheat to high. Brush and oil the grill grate.
Lightly brush the romaine lettuce leaves on both sides with olive oil (you’ll need about 1 tablespoon.) Brush the insides of the onion rolls with the remaining oil.
Arrange the bacon strips on the grill grate and grill until browned on both sides, 3 to 4 minutes per side. (Move them as needed to dodge any flare-ups.)
Grill the hamburgers until cooked to taste, about 4 minutes per side for medium (160°F on an instant-read thermometer.)
Grill the lettuce leaves over the hot fire until lightly browned, 30 seconds minute per side. Toast the onion rolls, cut side down, over the hot fire, 1 to 2 minutes.
To assemble, place a grilled romaine leaf on the bottom half of each onion roll. Top with a burger, then barbecue sauce, then a tomato slice, bacon, and more barbecue sauce. Top with the other onion roll half.