Place ham in a large pot or slow cooker and fill with enough water to cover. Bring to a boil, then reduce heat to low and simmer until fall-apart tender, 8 to 10 hours. Remove ham from water and allow to cool enough to handle.

Pull ham apart into shreds and place in the slow cooker. Stir in brown sugar and mustard. Cover and cook on Low until heated through, about 1 hour. Serve on dinner rolls.