Preparation Bring broth and ham hocks to boil in large pot. Cover, reduce heat to medium-low and simmer 15 minutes. Add diced potatoes, tomatoes with juices, onion, carrots, celery, barley, and oregano. Bring to boil. Reduce heat to medium-low; simmer uncovered until meat and barley are tender, about 1 hour. Using tongs, remove ham hocks from soup. Cut meat off bones and chop coarsely. Return meat to soup; discard bones. (Can be prepared 2 days ahead. Refrigerate uncovered until cold, then cover and refrigerate. Bring to simmer before continuing.) Add green beans; simmer until beans are tender, about 15 minutes. Season soup to taste with salt and pepper.
Preparation Bring broth and ham hocks to boil in large pot. Cover, reduce heat to medium-low and simmer 15 minutes. Add diced potatoes, tomatoes with juices, onion, carrots, celery, barley, and oregano. Bring to boil. Reduce heat to medium-low; simmer uncovered until meat and barley are tender, about 1 hour. Using tongs, remove ham hocks from soup. Cut meat off bones and chop coarsely. Return meat to soup; discard bones. (Can be prepared 2 days ahead. Refrigerate uncovered until cold, then cover and refrigerate. Bring to simmer before continuing.) Add green beans; simmer until beans are tender, about 15 minutes. Season soup to taste with salt and pepper.