Rinse and drain the soaked cannellini beans and set aside.
In a large pot, heat the olive oil and saute the carrots, celery and onions (the soffrito) until well-cooked but not browned, 8 to 10 minutes. Add the potatoes, cavolo nero and cabbage and saute with the soffrito until the cabbage is wilted, a few minutes. Add the tomatoes, breaking them up with a spoon, and then add the beans. Add enough hot water to cover the ingredients in the pot, and bring to a boil. Reduce the heat and simmer over low heat for 1 1/2 hours. Add the sliced bread to the pot along with 2 more cups of hot water. Continue cooking for another 30 minutes.
Add salt and pepper to taste. Serve with a drizzle of extra-virgin olive oil for garnish.
If reheating the next day: Reheat the soup slowly so as not to scorch the bottom of the pot. The soup should be thick. Bring to a simmer and adjust the seasoning to taste. Add a little more water if needed. Serve drizzled with extra-virgin olive oil.
Tuscan soup is made with unsalted bread. If the bread you find is Pugliese bread (made in the style of Puglia), it will need less seasoning as that bread is salted when baked. Unlike other Italian soups, ribollita never has Parmigiano-Reggiano on it. It is not served with cheese.