Make the sauce: Combine the garlic, chili powder, cayenne, allspice, 1/2 teaspoon salt and 1 teaspoon black pepper in a bowl. Whisk the ketchup, 1 cup water, the vinegar, mustard, molasses, brown sugar and Worcestershire sauce in a separate bowl. Heat the vegetable oil in a medium saucepan over medium-high heat. Add the garlic mixture and cook, stirring, until the oil turns brick red, about 1 minute. Add the ketchup mixture and bring to a gentle simmer; cook, whisking occasionally, 30 minutes.
Make the ribs: Soak 1 heaping cup hickory, mesquite or apple-wood chips in water, at least 30 minutes. Prepare a grill for indirect cooking over medium-low heat (about 250 degrees F): On a charcoal grill, bank the coals to one side; on a gas grill, turn on only one side of the burners. Cover the grate on the cooler side of the grill with aluminum foil. Close the grill lid. Position the ribs on a cutting board, meat-side down. Slip a small knife between the bone and membrane, then gently pull off the membrane. Sprinkle the racks with 1 teaspoon each salt and black pepper on both sides. Drain the wood chips. For a charcoal grill, scatter the chips directly over the hot coals; for a gas grill, put the chips in a smoker box and position over direct heat. Put the ribs meat-side up on the foil on the cooler side of the grill. Close the grill lid; bring the temperature back up and cook the ribs, undisturbed, 3 hours. (For a charcoal grill, adjust the vents, or add more hot, ashed-over coals as needed to maintain consistent heat.) Remove the ribs and close the lid. Wrap each rack tightly in foil, then return to the cooler side of the grill, meat-side down; close the lid and grill 2 more hours. Remove the ribs and carefully unwrap. Return to the cooler side of the grill, meat-side up; cook, basting generously with the sauce halfway through, until the meat is tender, about 1 more hour. Remove the racks and let rest a few minutes before slicing. Serve with the remaining sauce. Photograph by Con Poulos