Sort through the beans, discarding any debris. Rinse the beans under cold water and drain.
Place the rinsed beans into the slow cooker. Add diced onion, minced garlic, chopped celery, diced carrots, diced bell pepper, canned tomatoes, sliced sausage, bay leaves, dried thyme, and dried oregano.
Pour in the chicken or vegetable broth until all the ingredients are submerged. Stir gently to combine.
Cover the slow cooker and cook on low heat for 6 to 8 hours. Check the beans for tenderness; they should be soft but not mushy.
Around 30 minutes before serving, taste the soup and adjust seasoning as needed. Add salt, pepper, Cajun seasoning, or hot sauce to taste.
Once the beans are tender and the flavors have melded together, remove the bay leaves. Ladle the soup into bowls, garnish with chopped fresh parsley, and serve hot.