In a large bowl, mix together the ground beef, rice, egg, cilantro, onion, garlic, salt, pepper, and cumin. Form into meatballs about 1 inch in diameter.
In a large pot, bring the beef broth to a boil. Add the meatballs, one at a time, to the boiling broth. Reduce the heat to medium and let simmer for 20 minutes.
Add the diced tomatoes, carrots, potatoes, and zucchini to the pot. Continue to simmer for another 20 minutes, or until the vegetables are tender.
If using, stir in the chopped mint just before serving. Serve hot.