Step 1: In a large bowl, gently combine the ground meat, uncooked white rice, 1/4 cup finely chopped onion, 2 minced garlic cloves, fresh chopped mint, egg, 1 tsp cumin, 1/2 tsp salt, and 1/4 tsp black pepper. Mix just until combined, being careful not to overmix, which can make the meatballs tough.
Step 2: Roll the mixture into small, golf-ball-sized meatballs, approximately 1 to 1.5 inches in diameter. You should get about 25-30 meatballs. Set them aside on a plate.
Step 3: Heat the olive oil in a large pot or Dutch oven over medium heat. Add the chopped large onion and cook, stirring occasionally, until softened and translucent, about 5-7 minutes. Add the remaining 3 minced garlic cloves and cook for another minute until fragrant.
Step 4: Stir in the fire-roasted diced tomatoes (with their juices), tomato paste, beef broth, water, dried oregano, 1/2 tsp ground cumin, and the bay leaf. Bring the mixture to a gentle simmer, scraping up any browned bits from the bottom of the pot.
Step 5: Carefully add the prepared meatballs to the simmering broth. Gently stir to ensure they are submerged. Cover the pot and let the meatballs cook for about 15-20 minutes, or until they are cooked through and firm.
Step 6: Add the diced carrots, potatoes, and zucchini to the pot. Continue to simmer, uncovered, for another 15-20 minutes, or until all the vegetables are tender. Taste the soup and adjust seasoning with more salt and pepper as needed.
Step 7: Remove and discard the bay leaf before serving. Ladle the hot albondigas soup into bowls. Garnish generously with fresh chopped cilantro and serve immediately with lime wedges on the side for a squeeze of fresh citrus.