Make the sauce:
In a large saucepan, combine all the sauce ingredients. Heat over medium, stirring well to mix and dissolve the spices. Reduce the heat and simmer the sauce, uncovered, for 30 minutes, stirring occasionally.
Prepare the ribs:
Remove the thick membrane covering the bone side of the slab: Separate the membrane at one end of the slab by slitting it with a knife and forcing your fingers underneath it. Pull it down the length of the slab and discard it. Find the skirt -- the meaty flap that curves down the bottom of the meat side -- and trim off the thick membrane on its edge. Using a sharp knife, cut off the rib tips, cutting parallel to the bottom of the slab. Cut the rib tips into several pieces. Sprinkle the spice rub amply over both sides of the ribs and tips.
To prepare the fire, use a chimney starter to light 40 to 50 pieces of good-quality lump charcoal. When the coals are glowing, remove them from the starter and stack them on one side of the grill. (If you don’t have a chimney starter, stack the charcoal around some crumpled newspaper in a pyramid on one side of the grill and light the newspaper. The coals will be hot in 20 to 30 minutes.)
Add 3 or 4 hand-size pieces of apple or oak hardwood, preferably a little of both, to the stack of coals. Put a pie pan full of water next to the coals. Position the grate so that one of the holes is over the coals so you can add coals and wood chips as needed; otherwise, you’ll have to lift the grate.
When the coals are about 90% white, position the ribs on the grill anywhere but directly over the coals. Cover the grill with the lid, making sure that the air vent is on the side away from the fire. Cook the ribs for about 2 hours, maintaining a temperature of 230° to 250°F by adjusting the air vents on the grill as needed. (Opening the vents lets in more oxygen and raises the temperature.) Add more coal if the temperature drops below 230°F. (You’ll likely need to add 15 to 20 coals about 30 minutes after putting the ribs on.)
After about 2 to 2-1/2 hours, turn the ribs over. Add some more coals and a few more pieces of hardwood to the fire. Continue cooking the ribs about another 2 hours. To see if the ribs are done to perfection, take off one of the tip pieces and taste it. You can also tug on one of the ribs; if the meat is cooked, you should be able pull the rib away with ease.
If you want to glaze the meat with the barbecue sauce while they’re cooking, pour some of the sauce into a separate container (to avoid contaminating the whole batch) and brush it on both sides of the ribs about every 15 minutes during the last half hour of cooking. Alternatively, you can serve all of the sauce on the side.
Remove the ribs from the grill and let them sit for about 10 minutes. Cut the slabs into individual ribs and serve hot with extra barbecue sauce on the side.
You can also freeze the ribs in the slab for future great eating. Allow them to cool, wrap them in ample plastic wrap, and freeze. For best results, allow them to defrost in the refrigerator before reheating them in a 225°F oven for about an hour. I reheat mine right in the plastic wrap with no trouble at that low temperature. But you can also reheat them unwrapped in a foil-covered pan. If you want to reheat them on the grill, wrap them in foil.