Three-Bean Soup

Drain the white beans and combine with 7 cups water, the intact half of the onion, the 2 peeled garlic cloves and the bay leaf in a large saucepan. Bring to a boil, skim off any foam that rises and reduce the heat. Cover and simmer 1 hour, until the beans are just tender. Add salt to taste and freshly ground pepper. In a heavy soup pot or Dutch oven, heat the olive oil over medium heat and add the chopped onion, carrot and celery. Cook, stirring, until vegetables are tender, about 5 minutes, and add the garlic and the red bell pepper. Cook, stirring, until the garlic is fragrant, about 1 minute. Add the beans with their liquid and the bouquet garni, and bring back to a boil. Reduce the heat, cover and simmer 1 hour, until the beans and vegetables are tender and the broth is aromatic. Taste and adjust salt. Add freshly ground pepper. Meanwhile, rinse out the saucepan you started the beans in, fill halfway with water and bring to a boil. Fill a bowl with ice water. When the water in the saucepan comes to a boil, add salt to taste and drop in the green beans. Boil 4 minutes, and then transfer the beans to the ice water without draining the pot, using a slotted spoon or strainer. Drain the beans and cut in 1-inch pieces. Bring the water in the saucepan back to a boil and shell and skin the favas. Shortly before serving the soup, stir in the chopped parsley and mint, add the green beans and skinned favas and simmer for a few minutes. Serve, topped with Parmesan cheese if desired.