Heat 2 tablespoons of oil in a large, heavy-bottomed Dutch oven over medium heat. Add the diced onion, bell pepper, and celery. Sauté for 5-7 minutes until vegetables soften and onions become translucent.
Add the minced garlic and cook for another minute until fragrant. Then add the sliced andouille sausage and cook for 3-4 minutes until it begins to brown slightly.
Drain and rinse your pre-soaked beans, then add them to the pot. Stir in the bay leaves, thyme, oregano, Cajun seasoning, and cayenne (if using). Add the ham hock if you're using one. Mix everything together until the beans are well coated with the seasoning mixture.
Pour in the chicken stock or water, ensuring the liquid covers the beans by about an inch. Bring to a boil, then reduce heat to a gentle simmer. Cover partially and cook for 2½-3 hours, stirring occasionally.
When the beans are soft and creamy, remove the bay leaves and ham hock (if used). Take about ¼ cup of beans and mash them with a fork, then stir back into the pot to thicken the mixture. Add the butter and stir until melted.
While the beans are in their final 30 minutes of cooking, prepare your rice. Rinse the rice until the water runs clear. In a medium saucepan, bring 4 cups of water to a boil with salt and butter. Add rice, reduce heat to low, cover, and simmer for 20 minutes. Remove from heat and let stand, covered, for 10 minutes before fluffing with a fork.
Serve the beans over the rice, garnish with fresh parsley, and add hot sauce to taste.