For six as a first course:
Slice the leek (white and light green parts only) and chop the onion. Melt the butter in the oil in a pot over medium heat, add the leek and onion, and sauté, stirring occasionally, until the mixture begins to brown.
Meanwhile, clean and chop the Poblano, carrot, celery, and zucchini; mince the garlic; shred the cabbage; trim the green beans and cut into 1-inch pieces. Add the vegetables to the pot and cook for several minutes. Add the tomatoes, salt, and pepper, and continue cooking for several minutes longer. Add the stock, raise the heat, and bring to a boil. Cover the pot, reduce the heat, and simmer slowly for about two hours, adding the cannellini for the last few minutes.
Cover the soup with minced parsley and serve with grated parmesan.