1. In a large pot over medium heat, cook sausage, stirring and breaking up with a wooden spoon until no traces of pink remain, 6 to 8 minutes. Transfer meat to paper towels; drain fat from pot. Add olive oil, onion, garlic, celery and carrot and cook, stirring, until vegetables have softened, 6 to 8 minutes.
2. Stir in chicken broth, tomatoes with juice and 3 cups water and bring to a simmer. Add green beans and chard and simmer until very soft, about 20 minutes. Stir in beans, pasta and reserved sausage and simmer, stirring occasionally, until pasta is al dente, 8 to 10 minutes.
3. Stir in Parmesan and season with salt and pepper. Ladle into bowls and serve.