Preheat the oven to 300 degrees . Mix together the salt, pepper and paprika; sprinkle all over the pork and rub in.
In a large skillet or Dutch oven, heat the oil over medium-high heat. Add the pork and cook, turning occasionally, until browned, 8 to 10 minutes. Transfer to a 24-inch-long sheet of heavy-duty foil and double-wrap the pork.
Place the pork, skin side up, in a 9-by-13-inch baking dish; roast until tender, about 4-1/2 hours. Remove from the oven and carefully unwrap the top of the pork, revealing the skin. Increase the heat to 450 degrees and roast for 20 minutes more.
Transfer the roast to a large bowl, along with any juices. Using two forks, shred the pork. Add the vinegars, sugar and hot sauce; toss. Serve on the hamburger buns, topped with coleslaw, if using.