The usual go-to cut of pork for backyard barbecue is the pork shoulder, but in certain corners of South Carolina, many pitmasters swear by fresh ham. Fresh ham, cut from the hindquarters of the hog and sold unsmoked and unseasoned, is leaner than traditional barbecue cuts like shoulder. Rubbing salt over the entire surface and letting it sit overnight helped season it throughout and kept the meat moist. A double-pronged cooking approach did the trick: We smoked the meat on a grill for 2 hours before transferring it to a 300-degree oven to cook until it reached an internal temperature of 200 degrees. We then cranked the oven temperature up to 400 degrees and roasted the skin on a baking sheet until it was brown and crispy. This gave us plenty of crispy skin to mix in with the shredded ham. A vinegary mustard sauce, a hallmark of South Carolina barbecue, was just the contrast the sandwich needed. Plan ahead: The ham must be salted at least 18 hours before cooking. You’ll have about 2 1/2 cups of mustard sauce.