In a large Dutch oven or soup pot, heat the oil over medium high heat. Add the onion, garlic, celery, carrot, zucchini and potatoes and cook, stirring until the vegetables begin to soften, about 5 minutes.
Stir in the stock and tomatoes and bring to simmer. Simmer until the vegetables are almost cooked through, about 10 minutes.
Add the kale or chard, beans and pasta and simmer until the pasta is tender, about 10 minutes. Add the meatballs and basil and cook until the meatballs are is heated through, about 5 minutes. Season to taste with salt and pepper. Serve garnished with parmesan cheese.