Add the water and rinsed beans to a large pot and bring to a rolling boil over high heat. Stir in the salt, remove the pot from heat, cover, and let the beans soak for 1 hour.
After soaking, add the carrots, onion, celery, garlic, mustard powder, and bay leaves to the pot. Stir well, then add the ham hock. Bring the soup back to a boil, reduce the heat to low, and let it simmer gently for 1 hour.
Remove the ham hock from the pot and discard it. Stir in the chopped ham and continue simmering for about 30 minutes, until the soup is heated through and the flavors are well blended.
Season with ground white pepper to taste, remove bay leaves, and serve hot.