To prepare the soup, sort and wash the beans, and place in a large Dutch oven. Cover the beans with water to 2 inches above beans; cover and let stand 8 hours. Drain beans. Return beans to pan; cover with 6 cups water. Bring to a boil; cover, reduce heat, and simmer 1 hour and 15 minutes. Add 1/2 teaspoon salt; simmer 15 minutes or until beans are tender. Set aside.
Heat the olive oil in a stockpot over medium-low heat. Add potato, onion, and leek, and cook for 12 minutes, stirring occasionally. Stir in 1 teaspoon salt, kale, cabbage, chopped parsley, pepper, and minced garlic. Cover, reduce heat, and cook 30 minutes. Add bean mixture; cook 30 minutes.
To prepare garlic toast, place bread slices in a single layer on a jelly-roll pan. Broil for 2 minutes on each side or until toasted. Rub the toast with garlic halves. Ladle the soup into bowls; top with garlic toast, and sprinkle with cheese.