Spray a large (12 quart or larger) stockpot with nonstick spray. Heat over medium-high heat. Add carrots, onion, celery, and garlic; saute 8 minutes or until tender.
Add tomatoes with juice, breaking up tomatoes in pot with spoon. Add cabbage, green beans, broth, water, and a little salt and pepper (according to taste). Increase heat to high and bring to boil, stirring often.
Reduce heat to low, cover, and simmer for 10 minutes, stirring occasionally.
Increase heat to high again, and add zucchini and spinach leaves. Return to boil, and again reduce to low, cover, and simmer for 10 minutes or until all the vegetables are tender, stirring occasionally.
Correct seasoning if needed; serve hot or cool rapidly and refrigerate.