In large pot, heat oil over medium. Add onion, carrots, celery, red pepper flakes, rosemary, 1 1/2 teaspoons salt, and 1/4 teaspoon pepper. Cook until onion begins to turn golden, stirring constantly, about 5 to 8 minutes.
Add tomatoes. Cook until some liquid evaporates, about 2 minutes. Add potato, cabbage, beans and 7 cups water. Bring to boil and stir in green beans.
Reduce to simmer and cook until all vegetables are tender, about 20 minutes. Season with salt and pepper. Stir in garlic and basil. Serve sprinkled with Parmesan cheese.