Slice the ham into 5-6 inch size chunks, removing the bone and fat.
In a very large pot, add 3 cups of cider vinegar, 6 cups of water and 1 cup of sugar. Whisk until the sugar is dissolved.
Add the ham chunks to the liquid and bring to a boil.
Cover and reduce the heat to a simmer. Simmer for about 2 hours until the ham is tender and can easily be shredded. (NOTE: Leave the lid on as much as possible during cooking. If you need to add more liquid, add 1 part vinegar to 2 parts water.)
Grease a 9x13 baking dish. Carefully remove the ham from the pot and place the ham in the baking dish and start to pull it apart a little bit.
In a small bowl, mix together the remaining 1 cup brown sugar with the dry mustard.
Sprinkle the brown sugar evenly over the ham. Cover the baking dish with foil.
MAKE-AHEAD STOPPING POINT! At this point you can refrigerate the ham until you’re ready to bake it. The ham can be prepared up to 3 days in advance.