Soak the Beans: Sort and rinse the red beans. Soak them overnight in water or use the quick-soak method by boiling the beans for 2 minutes, then letting them sit for an hour. Drain before cooking.
Cook the Sausage and Ham: In a large pot or Dutch oven, heat the olive oil over medium heat. Add the sausage and cook until browned. If using ham, add it and cook for another 5 minutes. Remove the meat and set aside.
Sauté the Vegetables: In the same pot, add the onion, bell pepper, celery, and garlic. Sauté for about 5-7 minutes until softened and aromatic.
Add Spices: Sprinkle in thyme, bay leaves, cayenne pepper, salt, and black pepper. Stir to coat the vegetables in the spices.
Add Beans and Liquid: Add the soaked beans and chicken broth. Bring to a boil, then reduce heat and simmer uncovered for 1.5 to 2 hours, stirring occasionally. Add more liquid if the beans begin to dry out.
Finish the Dish: Once the beans are tender, return the cooked sausage and ham to the pot. Stir to combine. Adjust seasoning as needed and add hot sauce for extra spice, if desired. If using, add a splash of vinegar for balance.
Serve: Serve the Red Beans over cooked white rice and garnish with fresh parsley or green onions. Enjoy!