In a large Dutch oven, stir together the water, meaty crosscuts, bouillon granules, bay leaves, oregano, marjoram, and black pepper. Bring to boiling; reduce heat. Cover and simmer for 2 hours.
Remove the meaty crosscuts. When meat is cool enough to handle, cut it off the bones and coarsely chop. Discard bones.
Strain the cooking broth through a large sieve or colander lined with 2 layers of 100-percent cotton cheesecloth. Pour broth into a metal bowl; place bowl in ice water to solidify the fat in the broth. Skim off fat from broth. Return broth to Dutch oven.
Stir in meat, fresh tomatoes or undrained canned tomatoes, corn, potatoes, beans, carrots, green pepper, onion, and celery. Return to boiling; reduce heat. Cover and simmer about 30 minutes more or until vegetables are crisp-tender. Makes 4 servings.