Combine paprika, brown sugar, chili powder, cumin, thyme, salt and pepper. Untie roast if necessary. Rub spice mixture over pork; transfer to bowl or resealable plastic bag. Cover and refrigerate for at least 4 hours or for up to 24 hours.
In large ovenproof skillet, heat oil over medium-high heat; brown roast on all sides. Place in oven for 2 1/2 hours or until meat thermometer inserted in centre registers 160ºF (70ºC). Transfer pork to cutting board; tent with foil and let stand for 20 minutes to let cool. Using 2 forks or hands, pull pork into shreds and place in bowl.
Pour 1 1/2cups (375 mL) of the sauce over pork, tossing to coat. Pile onto rolls. Drizzle with remaining sauce.
Meanwhile, in saucepan, bring barbecue sauce, brown sugar, vinegar and hot pepper sauce to boil. Reduce heat and simmer, stirring occasionally, for 5 minutes.