Soak the beans overnight. Drain them and cook them in plenty of water, until al dente. Strain but keep the cooking water. Set aside.
Heat the oil on medium heat in a large sauce pan. Saute carrot, onion, leek and parsley until the onion is translucent and soft.
Add the tomatoes and stir. Tie together the rosemary and thyme with kitchen twine and put in the pan, securing the string to one of the handles.
Add all the prepared vegetables, the potato and some of the beans cooking liquid. Salt and let cook, on medium-low heat, adding more liquid as needed, about 30 minutes.
While the greeens are cooking, puree half of the beans in a blender or mixer. Set aside.
Once the vegetables are cooked, remove the thyme and rosemary and toss. Puree 1/3 of the greens in a blender or mixer, then put them back in the pan, together with the pureed and whole beans. Let cook for 5 to 10 minutes, and taste for seasoning. Add salt and pepper as needed.
Cut the bread slices in half. While the soup, which will be pretty thick, is still hot, ladle some in 6 bowls. Place the bread on top and cover with more soup. Drizzle some extra virgin olive oil and serve. Soup can be made a day ahead, re-heated and assembled.