Cut grilling cheese into four lengthwise slices, each about ½-inch-thick. Preheat grill to high. Cook cheese slices until grilled on both sides. Remove cheese to cutting board: cut into 1-inch pieces.
In large bowl combine black beans, garbanzo beans, diced tomato, cucumber, yellow pepper and red onion. In small bowl combine, cider vinegar, oregano, cumin and salt. Gradually drizzle in olive oil. Toss dressing with bean and vegetable mixture; stir in grilled cheese pieces.