This is a good make-ahead dish. Like most one-pot meals, the flavor is even better the second day.
Heat the oil in a large heavy gumbo pot on medium heat. When hot, add the flour and cook, stirring constantly until the roux turns brown.
When the roux has reached its color, add the onions, bell peppers, celery and garlic. Saute for 6 minutes.
Cut the chicken breasts into quarters and cover with plenty of Cajun spice mix. Add the chicken to the roux and vegetable mixture and saute for another 10 minutes. Stir the mixture constantly while cooking.
Carefully add the first carton of chicken broth and stir until the roux has dissolve with the liquid to make a gravy. Add more broth as needed to keep the gravy loose and easy to cook without sticking to the bottom of the pot.
Add all the spices from Tabasco sauce through the bay leaves to the mixture and cook on low until chicken has cooked through. About 40 minutes.
Add the sausage and cook for another 15 minutes or so. Add the green onions at the end. Serve over rice.