Heat oil in a large pot over medium. Add onions and garlic; cook, stirring occasionally, until onions are translucent, about 5 minutes. Add carrots, celery, and chard stems; cook, stirring occasionally, until chard stems are translucent, about 10 minutes. Add green beans and tomatoes. Season with 2 teaspoons salt; cook, stirring occasionally, until beans and tomatoes start to soften, 5 minutes.
Add zucchini, 5 cups water, Parmesan rind, and butter beans. Bring to a boil, then reduce to a simmer. Cook until all vegetables are softened, about 25 minutes, adding chard leaves in last 2 minutes of cooking. Season with salt and pepper. Serve immediately, topped with grated Parmesan and basil, or freeze up to 3 months.