Saute garlic in oil in Dutch oven. When garlic browned (about 10 minutes discard). Add chopped carrot and onion saute until they begin to color 3 to 5 minutes.
Add rosemary and tomato paste. Add beans with their liquid, and chicken broth. Simmer, uncovered, 2 minutes. Add pasta, stirring to distribute ingredients evenly. Cover and simmer, stirring occasionally for 8 minutes or until pasta is al dente (firm). Remove from heat. Let stand, covered, 10 minutes. Add salt if necessary. Stir vinegar into soup.
Combine: 1/2 cup grated Parmesan cheese and 1/4 cup finely chopped parsley. Sprinkle over top of soup.