For 8 servings:
For the beans: Soak beans in a large bowl with enough cold water to cover by 3 inches, at least 4 hours or overnight. Drain. Place 2 quarts water, beans and salt in large pot. Bring to boil over medium-high heat. Reduce heat to medium, cover partially and simmer until beans are tender, stirring occasionally, about 45 minutes.
For the soup: Heat 1/4 cup oil in a heavy large wide soup pot or Dutch oven over medium-low heat. Add leeks, onion, celery and carrots. Saute until onion is soft but not brown, about 12 minutes. Add kale, cabbage, parsley and minced garlic. Cover and cook over low heat until cabbage and kale are wilted, stirring occasionally, about 30 minutes. Add beans with their broth, tomatoes with juices and potatoes. Bring to boil over high heat. Reduce heat and simmer gently until potatoes are tender, about 25 minutes. Cool soup. Cover and refrigerate overnight. Bring soup to boil over medium-high heat, stirring occasionally. Season soup to taste with salt and pepper. Preheat broiler. Broil bread until golden brown, about 2 minutes per side. Rub cut side of garlic clove over bread. Brush with 3 tablespoons oil. Ladle soup into 8 bowls. Drizzle remaining oil equally over each. Place toasts atop soup. Serve soup, passing cheese separately.