1. Place beans in a large, heavy saucepan, add water to cover to a depth of 1 inch, and set over high heat. Add coarsely chopped onion, bring the pot to a boil, and then turn down to a simmer and let cook until the onion has almost disintegrated and the beans are almost tender, about 1 hour.
2. Drain the beans and onions, reserving the cooking liquid. Transfer about a cup of the liquid and about a cup of the beans (with some of the cooked onions) to a food processor. Buzz smooth and set aside.
3. Toward the end of the bean cooking time, heat the oil in a large, heavy soup pot over medium heat. Add the finely chopped onion and gently saute it until it begins to get limp but not brown, about 5 minutes. Add the carrot and celery, and saute until slightly tender, another 5 to 8 minutes. Add the garlic and saute until fragrant, 1 more minute more.
4. Add the beans and their cooking liquid to the vegetables in the soup pot. Then add the tomatoes, rosemary, and pureed beans, as well as about 3 cups of the boiling water. Bring the pot to a boil, turn down to a simmer, then cook, covered, untll the beans are fully tender, about another hour. Stir, and add more liquid as necessary- the beans should be covered by 1 to 3 inches of liquid of simmering liquid at all times.
5. When the beans are soft, add half the minced parsley, salt and pepper to taste, and another cup of boiling liquid to the pot. Bring back to a boil, uncovered, add the pasta, and cook, stirring frequently, until the pasta is tender, about 10 minutes. Remove from heat, adding more salt and pepper as needed.
6. Serve topped with cheese
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