Place kidney beans in a large bowl and cover with water by at least 2 inches. Soak overnight or for at least 8 hours. Alternatively, for a quick soak method, bring beans and water to a boil for 2 minutes, then remove from heat and let sit covered for 1 hour.

Dice the onion, bell pepper, and celery. Mince the garlic and set aside.

In a large, heavy-bottomed pot over medium heat, cook the sliced andouille sausage until browned on both sides, about 5 minutes. Remove the sausage and set aside, leaving the rendered fat in the pot.

Add the diced onion, bell pepper, and celery to the pot. Cook until vegetables have softened, about 5-7 minutes. Add the minced garlic and cook for an additional 30 seconds until fragrant.

Drain and rinse the soaked beans. Add them to the pot along with the bay leaves, thyme, Cajun seasoning, cayenne pepper, salt, and black pepper. Stir to combine.

Pour in the chicken broth or water. Add the ham hock if using, and return half of the browned sausage to the pot, reserving the rest for serving.

Bring the mixture to a boil, then reduce heat to maintain a gentle simmer. Cook uncovered for 2-3 hours, stirring occasionally, until beans are tender and the mixture has thickened. Add more liquid if needed.

When beans are tender, use the back of a spoon to mash about 1/4 of the beans against the side of the pot. This helps create a creamy texture.

Taste and adjust seasonings as needed. Remove bay leaves and ham hock (if used). Shred any meat from the ham hock and return it to the pot.

Spoon the beans over hot cooked rice. Top with the reserved browned sausage, chopped parsley, and sliced green onions. Offer hot sauce on the side.