In a small bowl, mix together the garlic powder, onion powder, brown sugar, salt, chili powder, cumin and black pepper. Rub into the meat all over and let sit uncovered in the refrigerator for at least 2 hours, preferably overnight.
Remove the rib and let it come to room temperature. Prepare grill for cooking over indirect heat. For gas grills (with 3 or more burners), turn all the burners to medium-high heat; after about 15 minutes turn off one of the middle burners and turn the remaining burners down to medium or off, to maintain the grill at about 250 degrees F. For charcoal grills, bank one chimney starter-full of lit and ashed-over charcoal briquettes to one side of the grill. Set up a drip pan on the other side to avoid flare-ups. (Be sure to consult the grill manufacturer's guide for best results.)
Lightly oil the grill grates. Place the rib on the grill over the cooler burners, and cook indirectly, meat-side up, for 5 hours. Wrap the rib in foil and cook for another 45 minutes. Remove the foil and cook for an additional 45 minutes to create a nice bark. Remove the rib and let it rest. Serve whole on the side of a foot-powered prehistoric car.
Go to your local butcher and ask for uncut beef back ribs. They are generally about a foot long.