In a Dutch oven over medium heat, cook sausage until browned, about 8 minutes.
Transfer sausage to a paper towel-lined plate.
Cook onion, bell pepper, and celery in rendered fat until softened, about 5 minutes.
Add garlic, oregano, thyme, salt, and pepper; cook until fragrant, about 30 seconds.
Add broth, beans, and bay leaf; bring to a boil. Simmer, covered, until beans soften, about 20 minutes.
Transfer mixture to a slow cooker.
Place rice and water in a foil-covered loaf pan; nestle into the slow cooker.
Cook on low for 4-5 hours or high for 3-4 hours, until beans are tender.
Remove loaf pan and set aside. Puree 1 cup of beans; stir puree and sausage into the slow cooker.
Cook on high until heated through, about 10 minutes.
Season with salt and pepper. Fluff rice with a fork before serving.