Place the beans in a large bowl or pot and cover with water by 2 inches. Let soak for at least 8 hours. Drain and set aside.
In a large pot, heat the vegetable oil over medium-high heat. Add the tasso and cook, stirring, for 1 minute. Add the onions and celery to the pot. Season with salt and pepper, and cook, stirring, until the vegetables are soft, about 4 minutes. Add the bay leaves, parsley, thyme, and sausage, and cook, stirring, to brown the sausage, about 4 minutes. Add the garlic and cook for 1 minutes.
Add the beans and stock, stir well, and bring to a boil. Reduce the heat to medium-low and simmer, uncovered, stirring occasionally, until the beans are tender and start to thicken, about two hours. Should the beans become too thick and dry, add more stock, about ¼ cup at a time.
Remove from heat and with the back of a heavy spoon, mash about ¼ of the beans against the side of the pot. Continue to cook until the beans are tender and creamy, 15-20 minutes.
Serve over rice, removing the bay leaves. Enjoy!