In a small bowl, combine the brown sugar, kosher salt, smoked paprika, black pepper, garlic powder, onion powder, chili powder, cayenne pepper, and mustard powder. Stir well with a fork to break up any clumps until you have an even, sandy mixture.

Pat the ribs dry with paper towels. If there is a thin membrane on the bone side, slide a butter knife under one edge, grip it with a paper towel, and pull to remove so the ribs absorb more smoke and turn out more tender.

Trim any large, hard pieces of fat from the pork shoulder, leaving a thin fat cap. Pat dry with paper towels. Lightly score the fat cap in a shallow crosshatch pattern so the rub and smoke can penetrate.

Rub a thin, even layer of yellow mustard all over the ribs and pork shoulder. This helps the dry rub adhere during the long smoke.

Generously sprinkle the dry rub over all sides of the ribs and pork shoulder. Gently press the rub into the meat rather than rubbing hard so it forms an even coating that will become the bark.

Let the seasoned ribs and pork shoulder rest at room temperature for 20–30 minutes. Meanwhile, fill the hopper of your pellet smoker with hardwood pellets and preheat to 225°F with the lid closed for about 15 minutes, until the smoker is producing thin blue smoke.

Place the pork shoulder in the center of the smoker grate, fat cap up. Place the ribs bone side down beside it, leaving space between pieces for smoke circulation. Close the lid.

In a spray bottle or small bowl, combine the apple juice, apple cider vinegar, and Worcestershire sauce. Set aside for spritzing during the cook.

Smoke the ribs and pork shoulder at 225°F for about 3 hours without opening the lid. After 3 hours, briefly open the smoker and spritz the meat with the apple juice mixture. Continue smoking, spritzing every 45–60 minutes to add flavor and moisture.

At around the 4–5 hour mark, when the ribs have good color and the meat is pulling back slightly from the bones, wrap them tightly in heavy-duty foil or butcher paper with a light spritz inside. Return the wrapped ribs to the smoker at 225°F for another 1–2 hours to help them become tender and juicy.

Use an instant-read or probe thermometer to check doneness. Cook the pork shoulder until it reaches 195–203°F internal temperature. The ribs are typically done around 190–200°F when a toothpick slides between the bones with little resistance. Expect 8–10 hours total for a 4–5 lb pork shoulder and 5–7 hours total for the ribs at 225°F.

Remove the ribs and pork shoulder from the smoker once they reach temperature. Let the wrapped ribs rest for 20–30 minutes. Wrap the pork shoulder in foil or butcher paper, then a towel, and rest for at least 45–60 minutes to allow the juices to redistribute.

Slice the ribs between the bones. Remove the bone from the pork shoulder and pull the meat into shreds. Taste and adjust seasoning with a pinch of extra rub or salt if needed. Serve with barbecue sauce on the side so guests can sauce to taste.