Preheat oven to 400 degrees F. Peel off the outer papery layer of the garlic bulbs. Cut off the top third of the bulbs, exposing the tops of the cloves. Place a sheet of foil on a flat surface; place bulbs in the middle of the foil. Drizzle bulbs with the 1 tablespoon olive oil; fold foil up and over to form a packet. Roast garlic in the oven for 30 to 35 minutes or until soft and cloves are pulling away from papery covering. Cool about 30 minutes or until garlic is cool enough to handle. Squeeze the garlic cloves from the bulbs into a small bowl; mash with a fork to form a paste.
In a large bowl combine the garlic paste, Parmesan cheese, onion, dried tomatoes, basil, pepper, and salt. Add ground beef and Italian sausage. Mix very lightly with a fork. Shape meat mixture into twelve 1/2-inch-thick patties, about 4 inches wide. Cut the mozzarella into six 1/4-inch slices. Top six of the patties with a mozzarella slice. Top each with one of the remaining six patties. Pinch edges of top and bottom patties together to form one large burger patty, sealing all holes.
For a charcoal grill, arrange medium-hot coals around a drip pan. Test for medium heat above the pan. Place patties on grill rack over drip pan. Cover and grill for 10 minutes. Turn burgers with a wide spatula. Grill about 10 minutes more or until done (an instant-read thermometer inserted into patties registers 160 degrees F.) (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect grilling. Place patties on grill rack away from heat. Cover and grill as above.)
Brush cut side of rolls with additional olive oil. During the last 1 to 2 minutes of grilling, place rolls, oil-sides down, on grill directly over heat to lightly toast. Remove burgers and rolls. Let burgers stand for 2 minutes before eating (the cheese inside is hot).
Serve burgers in rolls with spinach leaves and Olive Mayonnaise. If desired, garnish each burger with an additional spinach leaf and a ripe olive on a wooden skewer inserted into top of roll.
In a small bowl stir together mayonnaise, olive tapenade, and basil.