Sort through the beans, discarding any impurities or discolored beans. Rinse the beans, drain, and put into a large pot. Add hot tap water to cover by 2-3 inches. Bring just to a simmer and remove from the heat. Cover and let soak for 1-1½ hours. Drain, rinse, and drain again.

Return the beans to the pot and add 6 cups hot tap water. Rinse the ham shank or hock and add to the pot along with the yellow onion pierced with cloves. To assemble a bouquet garni, gather together the bay leaf, oregano or thyme sprigs, and parsley sprigs. Sandwich the bouquet between the 2 or 3 celery pieces and tie securely with kitchen string. Add to the pot. Bring just to a boil, reduce the heat to low, cover, and simmer for 45 minutes.

Meanwhile, core and peel the tomatoes. Cut in half crosswise and carefully squeeze out the seeds. Cut into small chunks; you should have about 1 cup. Set aside.

At the end of the 45-minute cooking time For the beans, remove the yellow onion and the bouquet garni and discard. Remove the ham shank or hock and, when cool enough to handle, cut the meat from the bone, removing and discarding any fat. Discard the bone and chop or shred the meat into small pieces. Return to the pot along with the tomatoes, carrot, and 1/2 cup of the sweet onion. Add the salt and freshly ground pepper to taste. Cover and simmer until the beans are completely tender, about 30 minutes longer.

Taste and adjust the seasonings. Serve in large individual bowls with the remaining sweet onion sprinkled evenly over the top.