Put the beans, water, tomatoes and their juices, garlic, celery, carrots, onion, barley, bay leaf, salt, Italian seasoning, pepper and porcini mushrooms in a slow cooker.
Cover and cook on low until the beans are quite tender and the soup is thick, about 8 hours.
Stir in the spinach, cheese and vinegar.
Cover and let the soup cook until the spinach wilts, about 5 minutes.
Taste and adjust seasonings.
Ladle the soup into warmed bowls and drizzle each serving with olive oil.