In a large mixing bowl, combine all the ingredients for the meatballs: ground beef, chorizo, egg, garlic, rice, cilantro, salt, pepper, and cumin. Mix well using your hands, ensuring everything is evenly incorporated.
Once the mixture is well combined, form meatballs that are about 1 1/2 inches in diameter. You should be able to make approximately 24 meatballs. Place them on a plate or baking sheet and set aside.
In a large stock pot, pour in the chicken broth and heat over medium-high heat. As it begins to warm, add chopped onion, celery, carrot, ground cumin, oregano, cilantro, and the can of diced tomatoes.
Stir the soup base well, allowing it to simmer for about 10 minutes. This step is essential as it helps the flavors to meld together beautifully.
After the initial simmer, gently drop the prepared meatballs into the soup. Be careful to avoid splashing, as the broth may be hot. Reduce the heat to a gentle simmer.
Let the meatballs cook in the soup for another 10 minutes. You'll notice them turning a lovely golden-brown as they absorb the broth's flavors.
Next, add the sliced zucchini to the simmering pot. This will not only enhance the flavor but also add a delightful texture to the soup.
Continue to let everything cook together for an additional 10 minutes. Keep an eye on the soup, and stir occasionally to prevent anything from sticking to the bottom of the pot.
Finally, taste the soup before serving. Adjust the seasoning with salt and pepper as needed. This is your opportunity to make it perfect!
Serve hot, garnished with extra cilantro if desired, and enjoy the heartfelt flavors of your homemade Albondigas Mexican Meatball Soup.