Italian Bean Ramen

Heat oil in a large, heavy pot over medium heat. Cook onion with salt, covered, stirring occasionally, until lightly browned, about 10 minutes. Add garlic and rosemary and cook, stirring, 1 minute. Add carrots, celery, potato, and water and bring to a boil. Reduce heat and simmer, covered, until carrots are tender, about 15 minutes. Puree 1/2 cup of beans with 1 cup of soup broth in a blender. Add to soup along with remaining cup beans and diced tomatoes, and bring to a boil. Add ramen noodles, then reduce heat and simmer, stirring occasionally, until just tender, about 3 minutes. Stir in parsley. Sprinkle 1 tablespoon Parmesan cheese over each serving of soup.