Bring a large pot of well-salted water to a boil over medium heat and set up a bowl of well-salted ice water. Add the shelled fava beans to the boiling water. Once the water has come back to a boil, cook the beans for 3 to 4 minutes. Remove them from the boiling water and immediately put them into the bowl of salted ice water. Once the beans have cooled completely, strain them from the ice water. Peel the tough, outer layer from the beans. In a large pan add the sausage( add the diced onions and celery and carrots. Cook the onions and celery until they become translucent and are very aromatic. Add the smashed garlic cloves stir and cook for 2 to 3 minutes. Stir in the lava beans. Taste for seasoning. Add the broth or stock, bay leaf, tomatoes or sauce and stir. Cook on low heat stirring occasionally for 2 hours. The longer the better! Ladle the soup into serving dishes, give them a little sprinkle of grated Parmesan and a drizzle olive oil. Serve with crusty artisan bread.