Warm the oil in a large saucepan or stockpot over medium-high heat. Add the onion, carrots, and celery and cook until tender but not brown, about 5 minutes.
Add the broth, water, potatoes, beans, cabbage, pasta, thyme, and salt. Increase heat to high and bring to a boil. Reduce heat to medium and simmer, partially covered, 15 minutes.
Add the tomatoes, beans, and broccoli and cook 5 to 10 minutes more or until all the vegetables are tender. Sprinkle with Parmesan.