1. Make the soup base: heat oil in Dutch oven or stock pot, sauté onion, carrot, celery, and minced rosemary. Season with salt and pepper. Cook until vegetables are softened, 10-15 minutes, stirring to prevent burning. Add oil as necessary.
2. Add garlic and cook for 1-2 minutes, until fragrant.
3. Add tomatoes, stir and cook until the liquid has cooked off, 5-7 minutes.
4. Add beans and whatever liquid you plan to use, as well as the parmesan rind if you have it. Bring to a boil, drop to simmer, cook for at least 10 minutes and up to 2 hours before adding final ingredients.
5. When ready to serve, add dried pasta and green beans, stir and cook for 10-15 minutes, until both are tender.
6. Stir in chopped herbs just before serving. Season with salt and pepper to taste.