Place beans in a large Dutch oven. Cover with water 2 inches above beans; soak 8 hours. Drain.
Sauté salt pork, garlic, and salt in hot oil in Dutch oven until fat is cooked from pork. Add chopped celery, carrot, and onion, and sauté 4 to 5 minutes or until tender. Add beans and 3 quarts water, and bring to a boil over medium-high heat. Reduce heat, and simmer, stirring occasionally, 1 hour and 30 minutes or until tender, adding hot water as needed to keep beans covered with liquid. Stir in peppers.
Process half of cooked beans in batches in a blender until smooth, stopping once to scrape down sides; return to Dutch oven. Add pasta, and cook over low heat, stirring constantly, until thoroughly heated. Serve with cheese.