Bring first 4 ingredients to a boil in a Dutch oven; reduce heat to medium-low, and cook 15 minutes. Drain through a sieve into a large bowl; discard solids.
Measure 1 cup beans, and mash with a fork in a small bowl. Reserve the remaining whole beans.
Heat oil in pan over medium heat. Add onions, carrot, and celery; cook 4 minutes. Add broth mixture, mashed beans, whole beans, tomatoes, and barley; bring to a boil. Reduce heat; simmer 15 minutes. Stir in spinach and black pepper; cook 5 minutes or until barley is tender. Sprinkle each serving with cheese.