Store-bought barbecue sauce, for serving (optional)
Preheat oven to 350 degrees, with racks in lower and upper positions. In a small bowl, combine sugar, cayenne, 1 tablespoon salt, and 1 teaspoon pepper.
Place pork in a 5-quart Dutch oven or large heavy-bottomed pot; rub with spice mixture.
In a medium bowl, combine vinegar, garlic, and 1/2 cup water; pour over pork. Cover pot, and place in oven on lower rack. Bake until pork is very tender and separates easily when pulled with a fork, 2 to 2 1/2 hours.
Transfer pork to a work surface, reserving pan juices. With two forks, shred meat. Transfer to a large bowl, and toss with pan juices to moisten (you may not need all the juices). Pile pork on rolls, and top with barbecue sauce, if desired.