Mix the paprika, garlic powder, brown sugar, dry mustard and salt together. In a small bowl, rub the spice blend all over the pork and marinate for at least 2 hours. or overnight, covered in the refrigerator. Preheat oven to 300°. Put the pork in a roasting pan and bake for about 6 hours. Basically roast the pork until it's falling apart and an instant-read thermometer inserted into the thickest part registers 170°. To make the barbeque sauce: Combine the vinegar, mustard, ketchup, brown sugar, garlic, salt, cayenne, and black pepper in a saucepan over medium heat. Simmer gently, stirring for 10 minutes until the sugar dissolves. Remove the pork roast form the oven and transfer to a large platter. Allow the meat to rest for about 10 minutes. While still warm take 2 forks and "pull" the meat to form shreds. Using 2 forks, shred the pork by steadying the meat with 1 fork and pulling it away with the other, separating out fat, and leaving very browned pieces! Put the shredded pork in a bowl. Pour 1/2 of the sauce on the shredded pork and mix well to coat. To serve, spoon the pulled pork mixture onto the bottom 1/2 of the hamburger bun, and top with spicy slaw (or serve on the side). Serve with pickle spears and the remaining sauce on the side.
