Combine the first 5 ingredients in a Dutch oven. Bring to a boil; cook for 10 minutes. Remove from heat. Remove chicken from broth; remove chicken from bones, discarding bones. Cut meat into bite-size pieces; return to broth. Discard bay leaves.
Add potato and next 9 ingredients (potato through tomatoes and chiles) to broth. Bring to a boil; reduce heat, and simmer 50 minutes or until potato is done. Remove from heat; stir in milk. Ladle soup into individual bowls, and sprinkle with cheese.