Combine first 3 ingredients in a large stock pot; bring to a boil. Skim surface frequently with a flat ladle to remove grayish scum. Reduce heat; cover and simmer 4 hours. Remove from heat, and set aside to cool.
Remove short ribs from stock; set stock aside. Remove meat from ribs; discard bones. Chop meat; cover and refrigerate.
Line a sieve with several layers of damp cheesecloth. Strain stock through cheesecloth into a bowl. Cover and refrigerate overnight. Carefully lift solidified fat from top of stock; discard fat.
Return stock and meat to stock pot; add remaining ingredients. Bring to a boil. Reduce heat; cover and simmer 1 hour or until vegetables are tender. Remove and discard cloves. Spoon soup into individual soup bowls; serve immediately.