Heat the olive oil in a 2-quart saucepan over medium heat. Add the celery, onion, bell pepper, garlic, and Creole seasoning, and cook until the vegetables soften, about 2 minutes.
Add the sliced sausage and cook until lightly browned, about 2 minutes.
Stir in the red beans, chicken broth, hot sauce, and thyme, and bring to a boil.
Reduce the heat to medium-low and simmer, stirring occasionally, until the sauce thickens, about 30 minutes.
Stir in the butter until melted, then mash a few beans against the side of the pan to thicken the sauce.
Spoon the beans over cooked rice and top with sliced green onions, if using.
Notes
Mash some of the beans. Near the end of cooking, press a few spoonfuls of the beans against the side of the pot and stir them back in. The starch they release is what turns canned beans into a thick, creamy sauce.Keep the simmer gentle. A low, steady simmer keeps the beans whole and creamy. A hard boil splits them and can turn the sauce pasty, so let it bubble slowly.Watch the salt. Creole seasoning blends and smoked sausage can be salty, and the amount of sodium varies by brand. Start with the amount of seasoning called for in the recipe, then taste at the end and add more if you feel it necessary.Let it rest a few minutes. Off the heat, the sauce thickens and the flavors settle as it sits. A short rest before serving gives you a thicker, richer bowl.If doubling this recipe, use a 3.5 to 4-quart pot.