Gather all ingredients.

Heat 2 tablespoons bacon grease in a large pot or Dutch oven over medium-high heat. Add sausage and sauté until browned on both sides, about 3 minutes. Remove from the pot with a slotted spoon and set aside. Reserve drippings in the pot.

Add chicken to the pot and sprinkle with salt and pepper. Cook, undisturbed, until chicken easily releases from the bottom and begins to brown, about 2 minutes. Push chicken to one side of the pot and add pork. Cook, crumbling with a spoon, until browned, about 3 minutes. Stir chicken and pork together and remove from the pan with a slotted spoon, and add to the reserved sausage.

Add onion, bell peppers, celery, and jalapeño to the pan and cook 2 minutes, stirring constantly to lift off any flavorful bits from the bottom. Reduce heat to medium and cook, stirring often, until well browned and very tender, about 25 minutes.

Add garlic to the mixture and continue cooking for 2 minutes. Stir in Cajun seasoning, thyme, and bay leaves.

Pour in 1 cup stock to deglaze the pan, making sure to scrape up any bits from the bottom of the pan. Stir in remaining 5 cups stock and bring to a boil. Add browned sausage, chicken and pork back into the pan; stir in rice and bring to a boil again. Reduce heat, cover, and simmer until rice is tender and most of the liquid has been absorbed, about 25 minutes. Add up to 1 cup additional stock if necessary if liquid is absorbed before rice is tender.