In a large Dutch oven or kettle (heavy pot) combine meat, bay leaves, salt, oregano, marjoram, pepper, and 8 cups water. Bring to a boiling; reduce heat. Cover and simmer for 2 hours.
Remove meat. When cool enough to handle, cut meat off bones and coarsely chop. Discard bones.
Strain broth through a large sieve or colander lined with 2 layers of cheesecloth (I don’t do this). Skim fat and return broth to kettle. (If I have time I will chill broth until the fat is congealed on top and just scrap it off.
Stir in meat, corn, tomatoes, potatoes, beans, carrots, celery, and onion. Return to boiling; reduce heat. Cover and simmer about 30 minutes or till vegetables are crisp-tender. Discard bay leaves.