1. Warm oil in a large pot over medium-high heat. Add carrot, onion and celery; cook, stirring often, until softened, 3 to 5 minutes. Add garlic; sauté 1 minute. Pour in broth, increase heat to high and bring to boil. Add both types of beans. Cover, reduce heat to low and simmer 5 minutes.
2. Add cauliflower, spaghetti, zucchini and tomatoes. Cook until vegetables are tender, about 8 minutes. Add parsley; season with salt and pepper. Garnish with Parmesan.