Place beans in a large bowl and add enough water to cover them by 2". Let soak for 24 hours. Drain.
Heat oil in a Dutch oven over medium heat.
Add the onion, celery, and carrots and saute until just starting to get tender.
Add the garlic and cook another 2 minutes.
Crumble in the dried thyme and black pepper and stir.
Add the ham, jowl bacon, chicken stock, bay leaves and 4 cups of water.
Bring to a boil then reduce to a simmer and continue simmering for an hour.
Add beans, butter, parsley, and Cajun seasoning and stir.
Bring back to a simmer and simmer for another 1 hours and 30 minutes or until the beans are done and the sauce has thickened. If the sauce gets too thick add more water or chicken stock.
Season with salt and serve.