Place beans in a bowl; add cold water to cover. Cover bowl; let soak 8 hours or overnight.
Heat oil in a Dutch oven over medium-high; add cabbage, potatoes, chard, leeks, carrots, garlic, salt, and pepper. Cook, stirring often, until vegetables are wilted, about 10 minutes. Add 14 cups water to cover vegetable mixture. Reduce heat to low, and simmer gently while preparing beans.
Meanwhile, drain beans. Transfer beans to a large pot; add water to cover by 2 inches. Add bouquet garni; bring to a boil over high. Reduce heat to medium-low; simmer 15 minutes. Drain.
Add drained beans and bouquet garni to vegetable mixture in Dutch oven. Add tomatoes, ham bone, and pork cheek. Bring to a boil over high. Reduce heat to low; simmer, stirring occasionally, until beans and vegetables are very tender, about 1 hour and 30 minutes. Remove and discard bouquet garni and ham bone. Ladle soup into bowls and serve.
