In a large saucepan, heat the oil. When the oil is hot, add the onions, celery, and bell peppers to the saucepan. Season the vegetables with salt and cayenne. Saute the vegetables for 5 minutes, or until the vegetables start to wilt. Add the bay leaves, thyme, ham hocks, and pork meat and saute for 5 to 6 minutes. Add the beans, garlic, and stock or water. Bring the liquid up to a boil and reduce to a simmer. Cook for about 2 hours, uncovered. Add more stock or water if the mixture becomes dry and thick. Use a wooden spoon to mash 1/4 of the mixture. Continue to cook, stirring occasionally, for about 1 1/2 hours, or until the beans are tender and creamy. Add more liquid if it is too thick. The mixture should be soupy, but not watery. Remove the bay leaves and thyme sprigs. To serve ladle into bowls with rice. Garnish with green onions.