Char the poblano peppers over a gas burner turning often, or under a broiler on a lined baking sheet turning once, and cook until the skin is completely black and blistered.
Quickly place the hot peppers in a bowl covered with plastic wrap or a tight fitting lid to steam and cool.
Remove the burnt skin by rubbing it off with a paper towel. Discard the seeds and membrane, and chop the flesh of the pepper into a small dice.
Heat the butter in a Dutch oven over medium heat. Add the onion, celery, bell pepper and saute about 5 minutes, or until they have softened. Add the garlic and spices and cook for another 30 seconds. Stir in flour, cook for about 2 minutes.
Whisk in the broth and bring to a boil, add the chopped poblanos, corn, chicken, lime juice and cilantro. Simmer until heated through. Taste and adjust seasoning.
Serve bowls of soup garnished with tortilla strips, radish, cilantro, jalapeno and cheese, if desired.
Store leftovers in the fridge for up to 5 days, or frozen for up to 3 months. Reheat gently in a pan on the stove or in the microwave.