This starts as a basic gumbo – cook a dark roux with flour and oil, add the Cajun trinity of diced onions, celery, and green peppers. Let the veggies cook for a few minutes then add chicken broth. I browned chicken thighs and fresh chorizo in a separate pan then added those to the simmering broth. The fresh chorizo is where this veers off the normal path. Alas, I had no more Andouille and it really wanted sausage. The recipe uses a homemade seasoning from this recipe. That NOLA site is a goldmine for this style of cooking and you can do worse than spending a while looking over all the recipes.
When the sausage and chicken are cooked through remove them to cool, slice the sausage and strip the chicken meat from the bones and add it all back to the pot. This will take a couple of hours. I did the roux atop the stove on a medium high heat and stirred it constantly lest it burn, using a flat wooden spatula to keep the bottom scraped. That took 20 minutes or so.