- Brown the andouille in a large heavy pot over medium heat, 5 minutes. Lift it out and set aside.
- Add the oil and flour to the pot. Cook over medium-low heat, stirring constantly with a flat wooden spoon, until the roux is the color of dark chocolate, 30 to 45 minutes.
- Add the onion, bell pepper and celery. Stir for 5 to 7 minutes as they soften and cool the roux. Add the garlic for 1 minute.
- Slowly pour in the warm stock, a ladle at a time, stirring until smooth.
- Add the whole chicken thighs, sausage, bay leaves, thyme, Cajun seasoning and cayenne. Simmer uncovered for 1 hour, skimming fat from the top.
- Lift out the chicken, shred it and return it to the pot. Simmer 15 minutes more. Season with salt.
- Stir in the green onions and parsley. Serve over rice, with filé powder at the table.