In a mixing bowl, combine the ground beef, rice, onion, garlic, egg, cumin, salt, pepper, and cilantro. Mix well until fully combined.
Shape the meat mixture into small meatballs, approximately 1-inch in diameter. You should get about 24 meatballs.
In a large pot or Dutch oven, bring the beef broth to a boil over medium-high heat.
Carefully add the meatballs to the boiling broth. Reduce the heat to medium and let the meatballs cook for about 10 minutes.
Add the diced tomatoes, carrots, potatoes, zucchini, peas, oregano, and chili powder to the pot. Stir well and bring back to a gentle simmer.
Cover the pot and cook for an additional 20-25 minutes, or until the vegetables are tender and the meatballs are cooked through.
Taste and adjust seasoning with salt and pepper if needed.
Serve hot with lime wedges on the side.