Make the rub: Mix all rub ingredients in a small bowl until no brown sugar clumps remain (if you want a finer rub, you can run it through a spice grinder).
Season the pork: Pat the pork dry. Spread a thin layer of yellow mustard for a binder (optional) over all sides. Coat heavily with the rub. Let it sit while you preheat the smoker, or wrap and refrigerate overnight.
Heat the smoker: Set your smoker to 275°F. Apple, cherry, or hickory wood all work well (I prefer a combination of cherry and apple for flavor and color).
Smoke the pork: Place the pork fat side up on the smoker. Smoke until the internal temperature reaches 165 to 170°F and the bark is dark and set, about 4 to 5 hours.
Spritz: After the first hour, spritz the pork with diluted apple cider vinegar and water every hour to keep the surface moist.
Build the braise: Spread the onion, garlic, apples, thyme, and bay leaf in a deep foil pan or braising pan. Whisk together the apple cider, chicken stock, apple cider vinegar, and whole grain mustard. Pour into the pan.
Braise the pork: Set the pork on top of the onions and apples. The liquid should come about one third of the way up the meat (you want some of the pork exposed to keep the bark texture intact). Cover tightly with foil.
Finish cooking: Return the pan to the 275°F smoker, or move it to a 275°F oven. Cook until the pork reaches 203°F and a probe slides in with no resistance, about another 3 to 4 hours.
Rest: Keep the pan covered and let the pork rest for at least 1 hour (2 hours is my preference) in a hot box or cooler.
Make the sauce: Lift out the pork. Strain the braising liquid, saving the apples and onions. Skim off the fat. Simmer the liquid in a saucepan until it reduces by about half and coats a spoon, 15 to 20 minutes. Taste and add salt if needed.
Pull and serve: Remove the bone and shred the pork. Toss with some of the reduced sauce. Serve with the braised apples and onions and the rest of the sauce on the side.