Step 1: In a large mixing bowl, combine the ground beef (or beef/pork mix), rinsed short-grain rice, 2 tablespoons finely chopped fresh mint, 2 tablespoons finely chopped fresh cilantro, 1/4 cup finely chopped white onion, 2 cloves minced garlic, one large egg, 1 teaspoon salt, and 1/2 teaspoon black pepper. Gently mix with your hands until just combined, being careful not to overmix to ensure tender meatballs.
Step 2: Roll the mixture into small, golf-ball-sized meatballs, about 1 to 1.5 inches in diameter. Place them on a plate or baking sheet as you form them. You should get approximately 20-25 meatballs.
Step 3: Heat 1 tablespoon of olive oil in a large stockpot or Dutch oven over medium heat. Add the remaining 1/2 cup of finely chopped white onion and sauté until softened and translucent, about 5-7 minutes.
Step 4: Add the remaining 2 cloves of minced garlic and cook for another minute until fragrant. Pour in the crushed tomatoes and chicken broth. Bring the mixture to a gentle simmer, scraping up any browned bits from the bottom of the pot. Season with salt and pepper.
Step 5: Add the diced carrots and diced potatoes to the simmering broth. Continue to simmer for about 10-15 minutes, or until the vegetables are slightly tender but not fully cooked.
Step 6: Carefully add the meatballs one by one into the gently simmering broth. Avoid a rolling boil. Once all meatballs are in, cover the pot and continue to simmer on low heat for about 15-20 minutes, or until the meatballs are cooked through and the rice inside is tender.
Step 7: Add the diced zucchini to the soup. Continue to simmer for another 5-7 minutes, or until the zucchini is tender-crisp.
Step 8: Taste the soup and adjust seasonings as needed. Ladle the hot soup into bowls and garnish generously with extra fresh cilantro. Serve immediately with lime wedges on the side for squeezing.