Sort and rinse dried beans, then cover with cold water (3-4 inches above beans). Refrigerate overnight or at least 8 hours. Drain and rinse before using.
Heat bacon grease or oil in Dutch oven over medium-high heat. Brown sausage slices for 5-7 minutes until golden. Remove with slotted spoon, leaving drippings.
Reduce heat to medium. Add onion, celery, and bell pepper. Cook 8-10 minutes until softened, scraping up browned bits. Add garlic and cook 1-2 minutes until fragrant.
Add drained beans to pot and stir to coat. Pour in stock or water, ensuring liquid covers beans by 1 inch. Add bay leaves, thyme, oregano, smoked paprika, cayenne, salt, black pepper, and white pepper (if using). Return browned sausage to pot.
Bring mixture to a boil over high heat (5-7 minutes). Reduce heat to low, partially cover, and simmer gently for 2-3 hours, stirring every 20-30 minutes. Add more liquid if needed to keep beans just covered.
Remove and discard bay leaves. Mash about one-third of the beans against the pot side using a wooden spoon or potato masher. Stir to create creamy consistency with some whole beans remaining.
Taste and adjust seasoning with additional salt, pepper, or cayenne. Remove from heat and let rest, covered, for 10-15 minutes to allow flavors to meld.
While beans rest, cook rice according to package directions. Serve by placing a generous scoop of rice in each bowl, ladling red beans and sausage over the top. Garnish with sliced green onions and hot sauce on the side.