Combine meat, tomatoes, onion, carrot, celery, allspice, 1 teaspoon salt, 1/4 teaspoon pepper, and water in a small Dutch oven; bring to a boil. Reduce heat to low; cover and simmer 3 hours. Remove from heat; cool.
Strain broth, reserving meat and vegetables for other uses, if desired. Cover broth, and refrigerate overnight. Skim off and discard fat; strain broth through several layers of damp cheesecloth. Return broth to Dutch oven, and set aside.
Grind liver and crackers together; place in a small mixing bowl. Add eggs, flour, remaining salt, and pepper, mixing until well blended. Bring broth to a boil. Drop liver dumpling mixture by 1/2 teaspoonfuls into boiling broth. Cook 1 minute.
Ladle broth and dumplings into warm soup bowls, and serve immediately.