Light about 3 quarts (45 briquettes) of charcoal and allow to burn until coals are fully ignited and partially covered with a thin ash layer, about 20 minutes. Arrange the coals, 2 to 3 briquettes high, far to one side of the grill. Set the cooking grate in place. Open the top and bottom grill vents halfway. Place the lid over the grill and let heat for 5 minutes. Meanwhile, drain the wood chips.
Position the rib racks, meaty side up, on the opposite side of the grill from the coals. Drop about 1/4 cup wood chips over the coals. Cover the grill, making sure to position the lid so the vents are placed over the ribs and opposite the coals, to help draw smoke through the grill and around the meat. Meanwhile, combine the apple cider and vinegar in a small sauce pot. Bring to a simmer, then remove from heat, cover and reserve.
After 30 minutes, turn the racks, switching positions and rotating 180 degrees. Add 1/4 cup wood chips to the coals.
After 1 hour, open the top and bottom vents completely. Baste the ribs with the cider/vinegar mixture, using a pastry brush or spray bottle. Turn the racks again and add another 1/4 cup of wood chips.
Continue to cook - making sure to turn the racks, baste the ribs and add wood chips every half hour, and add 12 new briquettes every hour (while still turning, basting and adding chips) – until the meat is very tender and starts to pull away from the bones, about 3 to 4 hours total.
Before removing the ribs from the grill, place each rack, one at a time, on the grate directly over the hot coals, cooking about 30 seconds on each side. Transfer to a cutting board, cover loosely with foil and allow to rest 20-30 minutes.
Slice the ribs between the rib bones and serve the barbecue sauce on the side.
Barbecue Sauce
Transfer this mixture to a blender and puree until smooth, about 30 seconds. Transfer back to the saucepot. Stir in the rest of the ingredients (ketchup, tomato sauce, vinegar, Worcestershire sauce, lemon juice, Tabasco sauce, liquid smoke, molasses, brown sugar, Dijon mustard, dry mustard and black pepper) and stir to combine. Bring to a boil over medium-high heat, then reduce the heat to low and simmer, uncovered and stirring frequently, until thickened to the desired consistency, about 15 minutes.