Mix brown sugar, chili powder, paprika, onion flakes, garlic powder, salt, black pepper, and dry mustard in a small bowl. Spice rub can be made up to a week in advance. This recipe make a cup; you will need about 3/4 cup for the pork.
Place a wire rack in a deep roasting pan. Pat pork roast dry. Cut four 1/2 inch deep slits evenly spaced on both sides of the roast. Set roast on the rack in the pan, fat side down. Coat heavily with some of the spice rub. Turn roast fat side up. Coat sides and top with the spice rub. Roast can be refrigerated uncovered overnight.
Heat oven to 250 degrees F. Place the pan with the pork in the oven. Pour 2 cups water into the pan, but not on the roast. Roast until a meat thermometer registers 170 degrees F and a fork inserted in several spots is easily removed, which will take 10 to 11 hours. Add more water to the pan as needed.
Transfer the roast to a cutting board. Allow the meat to rest, tented with foil, about 20 minutes.
Meanwhile set the roasting pan over medium heat and stir in the chicken broth. Heat to a boil and cook to reduce the juices slightly. Season to taste with salt and some of the remaining spice rub if desired.
Slice the pork very thinly. Serve hot, drizzled with some of the pan juices.