To make the roux, in a large Dutch oven over medium heat, combine the oil and flour. Cook, stirring constantly until becomes a reddish-brown color, approximately for 30 to 40 minutes. Be careful not to burn.
Add to the roux the onions, bell pepper and celery, stirring, about 5 minutes; add broth. Bring to a boil, stirring to incorporate roux, then reduce heat and simmer for 1 hour. Add salt, pepper and cayenne. Add turkey and sausage then simmer an additional 30 minutes. Should the gumbo become too thick, thin with additional broth or water. Skim from the top any fat that surfaces.
Add the green onions and the parsley. Serve over hot rice.