Ribollita

To make the beans, pick over them and discard any misshapen beans and stones. Rinse the beans, drain and place in a saucepan with the water. Bring to a boil over high heat, boil for 2 minutes, then cover and remove from the heat. Let stand for 1 hour. Drain and return to the saucepan with fresh water to cover by about 2 inches. Add the onion, garlic and bay leaf and bring to a boil over high heat. Reduce the heat to low and simmer, uncovered, until the beans are tender but not falling apart, about 1 hour. Add the salt during the last 10 minutes of cooking. Remove and discard the onion, garlic and bay leaf. Set the beans aside in their liquid.

In a large saucepan over medium heat, warm the 1/2 cup olive oil. Add the onions, celery, carrots and garlic and sauté, stirring occasionally, until the onions are tender and translucent, about 10 minutes. Add the chopped tomatoes and tomato paste and cook, stirring occasionally, for 5 minutes. Add the cabbage, the cooked white beans and their liquid, thyme, salt and pepper, and enough water just to cover the vegetables. Increase the heat to medium-high and bring to a boil. Cover, reduce the heat to low and simmer until all the vegetables are very tender, about 2 hours. Remove from the heat, let cool, cover and refrigerate for 8 hours or for up to 3 days.

Remove the soup from the refrigerator. Layer 2 or 3 bread slices in the bottom of a large, heavy-bottomed saucepan. Ladle in enough soup just to cover. Repeat the layers until all the bread and soup are in the pan, ending with the soup. Slowly bring the soup to a boil over low heat, stirring often to make sure that the bottom doesn't scorch and to break up the bread, 20 to 30 minutes. It should eventually dissolve and absorb the liquids completely, forming a very thick soup.

Scoop into warmed bowls and drizzle with the olive oil. Serve immediately.