Preheat the oven to 325°F. In a small bowl combine the brown sugar, paprika, salt cayenne, garlic powder and mustard powder. Rub the spice mixture all over pork roast.
Pour the broth, coffee and Worcestershire into a large Dutch oven. Place the pork roast in the pot, cover the pot with foil and then the lid. Braise the pork until it’s fork-tender and shreds easily, about 4 hours; baste with the braising juices about every hour.
Remove the lid and foil and let the roast stand until it’s cool enough to handle. Shred the pork and toss with barbecue sauce. Serve pork on Kaiser rolls with additional sauce on the side.