In large kettle or Dutch oven, combine water and beef base. Add beef ribs and onion quarters. Bring to a boil over medium-high heat; reduce heat. Simmer, covered, until meat is tender and falling off the bones (about 2 hours). Remove meat from broth; cool. Separate meat from bones cutting into smaller pieces; refrigerate, covered. Strain hot broth into shallow containers; refrigerate, covered, several hours or overnight. Remove fat from top of broth. Return broth and beef to large kettle. Stir in remaining ingredients. Bring to a boil over high heat. Reduce heat; simmer, covered, until vegetables are tender (20-25 minutes). Ladle into bowls.