Remove the ribs from the refrigerator 30 minutes before cooking. Pat completely dry with paper towels and trim any excess fat, leaving a thin layer for flavor.
Place the rack bone-side up and slide a butter knife under the thin silvery membrane at one end to loosen it. Grip it with a paper towel and pull it off in one piece.
Mix all dry rub ingredients in a small bowl. Brush both sides of the ribs with yellow mustard, then generously massage the rub into both sides, paying extra attention to the meaty side and crevices.
Let the rubbed ribs sit at room temperature for 20 minutes while you prepare the grill.
Arrange coals on one side only (or light burners on one side for gas), add soaked wood chips, and target a grill temperature of 225–250°F (107–121°C). Place a water-filled foil pan on the cool side to maintain moisture.
Place ribs bone-side down on the cool side of the grill, close the lid immediately, and resist peeking for at least 45 minutes. Add fresh coals and wood chips as needed to maintain temperature.
After 1 hour, lightly spritz the ribs with apple cider vinegar. Repeat every 45 minutes; look for the meat to begin pulling back from the bones around hour 2 and a deep reddish-brown color to develop.
After 2 hours, remove the ribs, place bone-side up on heavy-duty foil, drizzle with 2 tablespoons of apple cider vinegar, and seal tightly. Return to the cool side of the grill and cook for 1 more hour.
Unwrap the ribs, return bone-side down, and brush generously with BBQ sauce. Cook 15 minutes, flip and sauce the other side, then move over direct heat for 2–3 minutes until the sauce is sticky and slightly charred. Internal temperature should reach 195–203°F (90–95°C).
Transfer ribs to a cutting board, tent loosely with foil, and rest for 10–15 minutes. Slice between the bones, arrange on a platter, and brush with extra BBQ sauce if desired.