In a large bowl combine the ground beef, the breadcrumbs, the salt, the egg, and two-thirds of the barbecue sauce, and mix lightly. Shape the meat mixture into 6 patties. Grill the patties on a barbecue grill set over medium-hot coals until cooked through, 2 to 3 minutes on each side, brushing with the remaining barbecue sauce while grilling. Top each of the patties with two Velveeta slices, criss-cross style, and return the patties to the grill to allow the cheese to melt. Place a lettuce leaf and a tomato slice on each hamburger roll and top with a patty. Serve with the salad and vegetables.