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.
Notes
Ham Type:do not use a pre-sliced/spiral sliced ham. It will be very, very dry. Look for a cut of ham that is not sliced and still has the bone-in. The best cut I've found is a butt or shoulder cut (might be labeled shank, also). Ham Size: you can make a larger ham than 5-7 pounds; you'll need a larger pot to accommodate the ham (and will increase the sugar/mustard mixture accordingly). My friend, Mel, that gave me the recipe, boils her ham in a huge pot outside on her propane stove (like a camp chef-type stove). I only had my classic stovetop available and used my biggest pot with the 5-7 pound ham. Make-ahead: the ham can be boiled and shredded a few days in advance of baking. It can also be assembled with the brown sugar mixture a day ahead of time.Cooking Time: take care not to boil the ham TOO long or you'll end up with ham jerky and you don't want that. If you are worried about time, err on the side of taking it out at 2 hours (even if it means you are having to cut part of the ham away from the bone instead of it falling away). It should still be very tender.