Melt margarine in a heavy stockpot over medium heat. Add onion, carrots, and celery; sauté until beginning to soften, 3 to 4 minutes. Add broth, beans, tomatoes, potatoes, cabbage, parsley, tomato paste, garlic, and salt; bring to a boil.
Reduce the heat, cover, and simmer until vegetables are tender, about 1 hour. Add pasta and simmer for 30 minutes more. Adjust seasoning as needed.
Ladle into bowls and garnish with Parmesan cheese.
