Combine ground beef, egg, bread crumbs, rice, cumin, garlic powder, and salt in a large bowl. Mix well.
Bring chicken broth to a boil over medium heat in a large kettle.
Form the beef mixture into 1 inch meatballs, using about 1 1/2 tablespoons of meat for each.Turn the heat down under the chicken broth to a simmer and drop the meatballs into the broth. Simmer the meatballs in the broth for 20 minutes, until meatballs are cooked through.
Stir in the carrots, onion, celery, canned diced tomatoes with green chiles, tomato sauce, canned chiles, cilantro, garlic powder, oregano, and cumin.Simmer the soup for 1 hour to cook the vegetables and blend the flavors.
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