Place the ham in a large pot (larger than you think - the liquid is splashy while cooking) and cover with 2 parts water to 1 part vinegar until the ham is covered by at least an inch or two of liquid.
Bring to a boil over high heat, reduce the heat to medium and continue to simmer vigorously for 2-3 hours, until the meat easily falls off the bone. Add more time, as needed until the meat is tender. Also if the liquid reduces, add more during cooking so the ham stays mostly covered.
When finished cooking, carefully remove the ham from the pot to a rimmed sheet pan, discarding the liquid. Let the ham cool until it is easier to remove the meat from the bones.
In a small bowl, stir together the brown sugar and mustard.
Shred the ham, discarding the fat and bones, and place half of the ham in a 9X9-inch baking dish (or a similar size). Sprinkle half of the brown sugar mixture over the ham. Layer the rest of the ham on top and sprinkle with the remaining brown sugar mixture.
Cover the dish tightly with foil and bake at 325 degrees for 1 hour. Serve warm or at room temperature.
