Cook the rice in a large saucepan with 2 cups of water as per the package instructions; set aside when done.
In a large pot, heat the vegetable oil over medium heat. Add the sliced sausage and cook until lightly browned, about 3-4 minutes; remove sausage and set aside.
To the same pot, add the diced onion, bell pepper, and celery, cooking until softened, about 3-4 minutes.
Mix in the tomato paste, minced garlic, and Cajun seasoning, stirring until fragrant, roughly 1 minute.
Add the red beans, chicken broth, hot sauce, bay leaf, and the browned sausage back into the pot. Season with salt and pepper to taste. Bring the mixture to a boil, then cover, reduce heat, and let it simmer for 15 minutes.
Uncover the pot and continue to simmer for another 15 minutes to reduce the liquid and intensify the flavors.
If a thicker consistency is desired, mash some of the beans with a wooden spoon. Season as needed.
Serve the red beans hot over the cooked rice and sprinkle with fresh parsley for garnish.