Preheat grill for indirect, low, and slow grilling.
Use a paring knife to cut the first 1-2 inches of silver skin off the backside of the ribs, then use your fingers to peel away the rest.
Rub ribs with about a tablespoon of Dijon mustard on both sides.
Combine brown sugar, kosher salt, onion, paprika, garlic powder, pepper, chili powder, and dried mustard in a small bowl. Rub ribs completely with the spice mixture.
Place ribs directly on clean grill grate and grill for 2 hours, rotating every 45 minutes or so to ensure even cooking.
After two hours, remove ribs from the grill and wrap tightly in foil. Add ¼ cup of apple cider vinegar to each rib pack. Return to grill for another 2 hours, rotating every 30-45 minutes.
After the second cooking phase, remove the top piece of foil and brush ribs liberally with Harry & David Texas BBQ sauce. Return to grill (still leaving the bottom of the ribs in foil for easier moving). Continue to grill the ribs over indirect heat until they are fall-apart tender, another 90 minutes to 2 hours. Baste with BBQ sauce occasionally and rotate every 30 minutes to ensure even cooking and that the sauce doesn't burn.
When ribs are done, let cool for 10-15 minutes, then remove and chop into individual ribs to serve.