Heat the oil in a large heavy pot over medium-high heat. Add the sausage and cook until browned, about 5 minutes. Add the onions, celery and peppers. Season with salt and black pepper. Cook until the onions are soft and translucent, 3 to 5 minutes. Add the garlic and cook until fragrant, 45 to 60 seconds.
Add the beans and water to the pot. Add the cayenne, white pepper, smoked paprika, bay leaves and green onions. Bring the mixture to a boil, then reduce the heat to a simmer. Cook, uncovered, stirring occasionally, until the beans are tender, 1 to 1 1/2 hours.
Discard the bay leaves. Use a potato masher to mash the beans in the pot until the mixture looks creamy. Season well with hot sauce. Taste and adjust the seasoning with more salt and black pepper. Ladle into warmed bowls with cooked rice and serve with additional hot sauce on the side.