Cook chicken. Remove from heat. Cool. Bone chicken and put in fridge until needed. Reduce broth to 1 quart and set aside.
Finely chop vegetables. Heat oil in skillet. When oil is hot, add 3/4 cup of the flour and stir with whisk until dark brown but not burned. Remove from heat and set aside. This is your dark roux.
In a 2 quart pot, heat butter on hi. Add onions, bell peppers, celery, and garlic. Saute until onions just begin to wilt. Add rest of flour. Stir in well and continue to stir until flour starts to brown.This is your light roux. Add slowly 1 quart of broth until all is added. Stir with whisk until blended with roux.
Add dark roux. Stir in well until blended. Bring to boil. Add remaining ingredients except chicken. Reduce heat to maintain boil. Cover and simmer 30 minutes.
Add chicken and stir. Cover and simmer 5 minutes. Let stand covered 10 minutes. Serve over rice or your favorite pasta.
You can also substitute shrimp or other meat for the chicken