Heat the vegetable oil in a 7-quart Dutch oven over medium-high heat. Add the onion, bell pepper, celery, salt, and pepper. Cook, stirring frequently, until the onions and celery are semi-translucent and the bell peppers are tender, 6 to 8 minutes. Add the garlic and cook for 1 to 2 minutes, stirring constantly. Add the pickled pork, bay leaves, thyme, hot sauce, cayenne pepper, water, and beans to the pot and increase the heat to high. Cook, stirring frequently, until the mixture comes to a boil, approximately 6 to 8 minutes.