Combine all of the rub ingredients together and coat the meat in the rub. Cover and marinate in the fridge for 24 hours.
Preheat the oven to 475°F. Place the pork on a roasting pan fat side up and roast for 15-20 minutes, until the top starts to brown. Reduce the heat to 300°F, and cook for 2 hours, until the meat is very tender and registers 180°F on an instant read thermometer.
Meanwhile, make the BBQ sauce by placing all of the ingredients in a blender and processing until smooth.
Remove the pork from the oven and rest for 15 minutes, covered. Then shred the meat and toss with the BBQ sauce.
To make the slaw, combine the mustard, mayonnaise, vinegar, sugar, salt and pepper in a large bowl. Fold in the cabbage, onion and carrots.
To assemble sandwiches, place Mustardy BBQ Pork Shoulder on buns, top with cole slaw and more mustard sauce if you like. Serve with pickles and potato chips on the side.