Heat the olive oil in a large stockpot. Add the onions and cook over low heat until soft but not browned. Add the carrots, celery, zucchini, potatoes, cabbage, beef broth, and Parmesan rind. Over high heat, bring to a boil. Reduce heat to low, cover, and simmer 2 hours, stirring occasionally. Add the tomatoes, white beans, green beans, and salt. Simmer 30 minutes more. Serve with the grated Parmesan.
KEEP IT: If you make a double batch so you can freeze half, remove the Parmesan rind before ladling the soup into containers or heavy-duty zipper bags. Freeze them up to 6 months. The soup can be thawed and heated in the microwave.