Dissolve 3 tablespoons salt in 4 quarts cold water in large bowl or container. Add beans and soak at room temperature for at least 8 hours and up to 24 hours. Drain and rinse well.
Heat bacon in a large Dutch oven over medium heat, stirring occasionally, until browned and almost fully rendered, 5 to 8 minutes. Add onion, green pepper, and celery; cook, stirring frequently, until vegetables are softened, 6 to 7 minutes. Stir in garlic, thyme, paprika, bay leaves, cayenne pepper, and 1/4 teaspoon black pepper; cook until fragrant, about 30 seconds. Stir in beans, broth, and water; bring to boil over high heat. Reduce heat and vigorously simmer, stirring occasionally, until beans are just soft and liquid begins to thicken, 45 to 60 minutes.
Stir in sausage and 1 teaspoon red wine vinegar and cook until liquid is thick and beans are fully tender and creamy, about 30 minutes. Season to taste with salt, black pepper, and additional red wine vinegar. Serve over rice, sprinkling with scallions and passing hot sauce separately, if desired.
NOTE: Times are longer at altitude. If you are pressed for time you can “quick-brine” your beans. In step 1, combine the salt, water and beans in a large Dutch oven and bring to a boil over high heat. Remove the pot from the heat, cover, and let stand 1 hour. Drain and rinse the beans and proceed with the recipe. If you can’t find andouille sausage, substitute kielbasa. Tasso can be difficult to find, but if you use it, omit the bacon and paprika in step 2 and cook 4 ounces finely chopped tasso in 2 teaspoons vegetable oil until lightly browned, 4 to 6 minutes, then proceed with the recipe. In order for the starch from the beans to thicken the cooking liquid, it is important to maintain a vigorous simmer in step 2. The beans can be cooled, covered tightly, and refrigerated for up to 2 days. To reheat, add enough water to the beans to thin them slightly.
