In a 4- to 5-quart pan, combine onion, carrot, tomatoes and their juices, 5 1/2 cups broth, and 1/2 cup water. Set pan over high heat and cover.
Meanwhile, in a bowl combine remaining 1/2 cup broth, beef, rice, flour, egg, 1/4 teaspoon salt, and 1/2 cup cilantro. Mix with your hands to blend well.
Uncover broth and vegetables and drop meat in 1 tablespoon portions into pan. When soup boils, reduce heat to a gentle simmer, cover pan, and cook 20 minutes.
Stir remaining cilantro into soup and ladle into bowls. Add salt to taste.