Combine the coffee, salt, chili powder, onion and garlic powders, coriander, pepper and cinnamon in a bowl. Mix with your fingers, breaking up any lumps. Set aside.
Remove the thin, papery membrane from the back of each rack of ribs. Turn the racks meat side down and insert a sharp implement, such as the tip of a meat thermometer, under the membrane (the best place to start is right next to the first rib bone). Using a dishcloth or pliers to gain a secure grip, pull off the membrane. Place the ribs on a baking sheet. Sprinkle the rub on both sides of the ribs, rubbing it into the meat. Cover the ribs and marinate for at least 1 hour or for up to 4 hours.
Melt the butter in a saucepan. Add the vinegar, bourbon and coffee and gently simmer for 1 minute. Whisk in salt and pepper to taste. Let the mixture cool to room temperature.
Set up the grill for indirect grilling and preheat to moderate (325° to 350°). Oil the grill grate. Arrange the ribs, bone side down, in the center of the grate over the drip pan away from the heat. If working on a charcoal grill and using wood chips, toss half on each mound of coals. Cover the grill and cook for 45 minutes.
Mop or brush the ribs on both sides with mop sauce. Cover the grill and continue cooking until the ribs are well browned and cooked through, yet tender enough to pull apart with your fingers, 1/2 to 3/4 hour more (1 1/4 to 1 1/2 hours in all). Mop the ribs once or twice more and, if using a charcoal grill, replenish the coals as needed. When the ribs are cooked, the meat will have shrunk back from the ends of the bones by about 1/4 inch. During the last few minutes, brush the ribs on both sides with Café au Lait Barbecue Sauce and move them directly over the fire. Sizzle the sauce on the ribs for 1 to 2 minutes per side.
Transfer the ribs to a large platter or cutting board. Cut the racks in half, widthwise (or into individual ribs). Serve at once with the remaining Café au Lait Barbecue Sauce on the side (or drizzled over the ribs if desired).