Place dried kidney beans in a large bowl, cover with at least 3 inches of cold water, and soak at room temperature for 8–12 hours or overnight. Drain and rinse thoroughly before cooking.
Dice the onion, celery, and bell pepper into uniform ¼-inch pieces, and mince the garlic cloves finely.
Heat 2 tablespoons of vegetable oil in a large Dutch oven over medium-high heat, then add sliced andouille in a single layer and cook 3–4 minutes per side until deeply browned. Remove with a slotted spoon and set aside, leaving the fat in the pot.
Reduce heat to medium, add the onion, celery, and bell pepper to the pot, and cook for 8–10 minutes until softened. Add garlic and cook 1 more minute until fragrant.
Add drained beans, bay leaves, thyme, smoked paprika, cayenne, and black pepper, then pour in chicken broth — the liquid should cover the beans by about 2 inches (add more if needed).
Increase heat to high and bring to a rolling boil; let it boil for 10 minutes, skimming off any foam that rises to the surface.
Reduce heat to low, partially cover the pot, and simmer for 2–2½ hours, stirring every 30 minutes, until beans are tender and the liquid has thickened.
Use the back of a wooden spoon to mash about a quarter of the beans against the side of the pot, then stir them back in to create a thick, creamy consistency. If too thick, add a splash of broth; if too thin, simmer uncovered 15–20 more minutes.
Return the browned andouille to the pot, stir to combine, and heat through for 5–10 minutes. Taste and adjust salt and cayenne, then remove bay leaves.
Spoon cooked white rice into individual bowls, ladle the red beans and sausage generously over the top, and garnish with sliced green onions. Serve with hot sauce on the side.