Place the peppers under broiler and cook about 3-4 minutes per side, until slightly charred but not burnt. Remove and let cool.
Heat oil, butter or margarine in a large stock pot. Season the chicken with blackening seasoning and add to skillet. Cook until both sides are blackened and chicken is fully cooked. Remove from pot.
Add onions to pot and cook for 2-3 minutes. Stir in corn and potatoes. Season with salt, pepper and cumin. Cook for 5 minutes.
Dice chicken and peppers and add to the pot. Stir to combine and add chicken stock. Bring to a slow boil, cover and cook as long as desired, but at least 30 minutes. Just before serving soup, melt butter or margarine in a small pot. Stir in flour and cook 2 minutes. Add 1 c. milk, bring to a boil and cook until thickened. Bring soup back to a boil, stir in roux and let boil until soup is thickened.
Divide soup into bowls. Top with a generous amount of shredded cheese, sour cream and fried tortilla strips.