Pulled Pork Sandwiches

Name: Pulled Pork Sandwiches
Ingredients: 6 tablespoons paprika; 3 tablespoons granulated sugar; Scant tablespoon onion powder; Kosher salt and coarsely ground pepper; 1 10-to-12-pound boneless pork shoulder or Boston butt, rinsed and dried; 12 soft hamburger buns, split; Coleslaw, for serving; 2 cups ketchup; 1/4 cup packed light brown sugar; 1/4 cup granulated sugar; Freshly ground pepper; 1 1/2 teaspoons onion powder; 1 1/2 teaspoons dry mustard; 2 tablespoons fresh lemon juice; 2 tablespoons Worcestershire sauce; 1/2 cup apple cider vinegar; 2 tablespoons light corn syrup