HEAT 1 tablespoon oil in cast iron 5-quart fryer, over medium heat. Add chorizo and cook 2 to 3 minutes, using back of spoon to break into pieces. Add chicken. Cook 2 minutes. Add onion, celery, carrots, poblano pepper and salt and cook 3 to 4 minutes, stirring occasionally. Add garlic. Cook 1 minute. Add 2 tablespoons oil. Stir in flour. Cook 1 minute. Add tomatoes and chicken broth. Stir well, scraping bits off bottom of pan. Cover. Bring to a boil for 10 minutes. Uncover and simmer 15 to 20 minutes.
STIR together cornbread mix, lime peel, milk, sour cream and 1/2 cup cilantro in medium bowl. Mixture will be thick. Set aside 10 minutes to ensure liquid is absorbed into cornmeal. Drop by tablespoonfuls into simmering soup. Cover and cook 8 to 10 minutes, or until puffed and firm.
TO SERVE, spoon a couple dumplings into each bowl and ladle soup around dumplings. Garnish with sour cream, cilantro, avocado and/or a squeeze of lime juice.