Rinse the beans, sorting out any broken or discolored ones.
In a large pot over high heat, bring the water to a boil.
Add the salt and the beans and remove from heat.
Let beans sit in the hot water for at least 60 minutes.
After the 60 minutes of soaking, return the pot to high heat and place the ham bone, carrots, celery, onion, garlic, mustard and bay leaves in the pot.
Stir well, bring to a boil, reduce heat to low and simmer for 60 more minutes.
Remove ham bone and discard. Stir in the chopped ham and simmer for 30 more minutes.
Season with ground white pepper to taste.