Fully submerge the black beans in cold water and allow to soak until doubled in size, at least 12 hours.
Simmer the ham hocks in the stock until very tender, 1½ to 3 hours, adding more stock as needed to maintain a level of 3 quarts. Remove the cooked ham hocks from the broth. Reserve the broth. Dice and reserve the meat from the ham hocks, discarding the bones