In a medium saucepan cook onion slices and garlic in hot olive oil over medium heat, covered, for 10 to 15 minutes or until onion is very tender, stirring occasionally; set aside.
For a charcoal grill, arrange medium-hot coals around the edges of the grill. Test for medium heat in the center of the grill. Toast one side of each bread round directly over the coals for 1 to 2 minutes. Remove from grill. Top toasted side of each bread round with onion mixture, sliced tomato, mozzarella cheese, and Romano cheese.
Return bread rounds to center of grill (not directly over coals). Cover grill. Grill for 5 to 10 minutes or until cheese is melted and toppings are heated through. Remove from grill and top with basil before serving.