Place water and beans in a large pot; bring to a boil over high heat. Stir in salt and remove the pot from heat; cover, and let stand for 1 hour.
Add carrots, onion, celery, garlic, mustard, and bay leaves to the pot with beans; stir well. Add ham hock and bring to a boil; reduce heat to low and simmer for 1 hour.
Remove ham hock and discard. Stir in chopped ham and simmer for 30 minutes. Season with ground white pepper to taste.