Preheat oven to 400° F.
Combine the oil and flour in a large heavy-bottom pot and heat over medium-high heat.
Stirring slowly and constantly for 20 to 25 minutes, make a roux, the color of milk-chocolate.
Add the onions, celery, and bell peppers and continue to stir until soft, or until the roux looks like dark chocolate, whichever comes first.
Add the sausage, salt, cayenne and continue to stir for 3 to 4 minutes.
Add water to cover and stir until the roux mixture and water are well combined, then add the bay leaves.
Bring to a boil, then reduce heat to medium-low.
Cook, uncovered, stirring occasionally, for 1 hour.
Season the chicken well on all sides with the rub; cover all the sides of the chicken chunks.
Add to the pot and bring to a simmer.
Place in oven and simmer slowly until the liquid is thickened and reduced, generally around 1-2 hours.
Remove from the oven and let sit for a few minutes. Then skim off all the fat from the surface.
Remove all the bay leaves.
If serving the next day, cool down to room temperature, refrigerate overnight and skim off the fat.
Before serving, reheat if it was refrigerated, garnish with parsley and green onions, and serve in deep bowls over white rice.
