Rinse the dried red kidney beans under cold water. In a large bowl, cover the beans with water and let them soak overnight. Drain and set aside.
In a large pot or Dutch oven, heat the vegetable oil over medium heat. Add the diced onion, bell pepper, celery, and garlic. Sauté for about 5 minutes, until the vegetables are softened.
Add the sliced sausage to the pot and cook for an additional 5-7 minutes, until the sausage is browned.
Stir in the soaked and drained beans, Cajun seasoning, thyme, bay leaves, black pepper, cayenne pepper (if using), and chicken or vegetable broth. Bring to a boil.
Reduce the heat to low and cover the pot. Let it simmer for about 1.5 hours, stirring occasionally, until the beans are tender and creamy. If the mixture becomes too thick, add a little water or broth to reach your desired consistency. Season with salt to taste.
While the beans are cooking, prepare the rice according to the package instructions or in a rice cooker.
Once the beans are cooked, remove the bay leaves and taste for seasoning adjustments. Serve the red beans over a scoop of white rice.
Garnish with chopped green onions and serve with hot sauce on the side if desired.