Score both sides of the pork shoulder to allow the marinade seasonings to get inside the pork.
Rub the dry rub all over the pork shoulder and inside the slits.
Add apple juice, apple cider vinegar, sugar, hot sauce and liquid smoke. Transfer the pork shoulder and all the liquid marinade inside a plastic bag. Marinate in the refrigerator overnight or best for 24 hours.
Heat up the oven to 250 °F (121 °C).
Transfer the pork shoulder onto a few sheets of heavy duty aluminum foil. Discard the liquid marinade.
Combine the dry rub and brown sugar in a small bowl and rub all over the pork. Wrap tightly with the aluminum foil. Make sure there is no leakage. Place the pork shoulder in a roasting pan with rack (preferred) or a deep baking pan, with the aluminum foil opening side up. This will prevent the pork jus from leaking out.
Slow roast the pork shoulder in the oven for 6 hours, recommended. (You may bake it at 350 °F (176°C) for 3 hours if you are pressed for time.)
In the meantime, heat up the BBQ sauce in a small sauce pan on low heat. Add the brown sugar, stir to mix well. Set aside.
Remove the pork shoulder from the oven, unwrap the aluminum foil and broil each side of the pork shoulder for 1-2 minutes, or until both sides are slightly charred.
Close off the aluminum oil, set aside and let cool for 30 minutes.
Discard the pork bone, shred and pull the pork with hands or using 2 forks. Reserve every bit of the pork jus inside the aluminum foil or on the roasting pan/baking pan. Spoon the pork jus all over the pulled pork.
How to Make Smoked Pulled Pork?
To smoke the pulled pork, heat up a stovetop smoker and add 1 tablespoon of wood chips in the middle of the smoker. Place some pulled pork on aluminum foil. Cover the lid and place the smoker on a burner on medium heat. Smoke for 5 minutes. Remove from heat and remove the pulled pork from the smoker after 10 minutes.
To serve, drizzle the BBQ sauce generously over the pulled pork. To make pulled pork sandwiches, stuff a slider bun or burger bun with pulled pork, top with BBQ sauce and coleslaw.