In a 4-quart Dutch oven, heat oil over medium heat. Add onion, celery, carrots, and garlic; cook for 5 minutes.
Stir in broth, squash, and undrained tomatoes. Bring to boiling; reduce heat. Cover and simmer for 20 minutes. Add beans, zucchini, broccoli, oregano, salt, and pepper; cook for 5 minutes more. If desired, sprinkle each serving with Parmesan cheese.
Variation: Slow Cooker Version: Omit olive oil. In a 3- ½- to 4-quart slow cooker combine onion, celery, carrot, garlic, broth, squash, tomatoes, beans and dried oregano (if using). Cover and cook on low-heat setting for 7 to 8 hours or on high-heat setting for 3- ½ to 4 hours. If using low-heat setting, turn cooker to high-heat setting. Add zucchini, broccoli, fresh oregano (if using), salt and pepper. Cover and cook 30 minutes more. Serve as above.