Place the beans in a large bowl or pot and cover with water by 2 inches. Let soak for 8 hours or overnight. Drain and set aside.
In a large pot, heat the bacon grease over medium-high heat. Add the tasso or ham and cook, stirring, for 1 minute. Add the onions, celery and bell peppers to the grease in the pot. Season with the salt, pepper, and cayenne, and cook, stirring, until the vegetables are soft, about 4 minutes. Add the bay leaves, parsley, thyme, sausage, and ham hocks, and cook, stirring, to brown the sausage and ham hocks, about 4 minutes. Add the garlic and cook for 1 minute. Add the beans and stock or water, stir well, and bring to a boil. Reduce the heat to medium-low and simmer, uncovered, stirring occasionally, until the beans are tender and starting to thicken, about 2 hours. (Should the beans become too thick and dry, add more water, about 1/4 cup at a time.)
Remove from the heat and with the back of a heavy spoon, mash about 1/4 of the beans against the side of the pot. Continue to cook until the beans are tender and creamy, 15 to 20 minutes. Remove from the heat and remove the bay leaves. Serve over rice and garnish with green onions.