For the turkey: One to two days before cooking, combine the sugar, 1/4 cup kosher salt and 1/2 teaspoon ground black pepper in a small bowl. Rub this mixture all over the turkey, including under the breast and thigh skin and inside the cavity. Refrigerate uncovered or lightly covered with plastic wrap.
For the cranberry bbq sauce: Heat the oil in a medium saucepan over medium heat. Add the onion and a pinch of salt. Cook until the onion is very soft and translucent, about 8 minutes. Add the garlic and paprika and cook, stirring frequently, 2 minutes. Stir in the cranberries, apple juice, ketchup, light brown sugar, molasses, vinegar, Worcestershire sauce, dry mustard, chipotle pepper, 3/4 teaspoon salt and a few grinds of pepper. Simmer until the cranberries start to burst, about 12 minutes. Transfer to a food processor and blend until very smooth. Reserve half for serving with the turkey. (You can make this sauce the day before and keep it refrigerated.)
Half an hour before cooking, remove the turkey from the refrigerator. Preheat a grill for indirect cooking over medium heat (about 350 degrees F). 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. 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.)
Pat the turkey very dry with paper towels. Brush the turkey all over with oil and sprinkle lightly with salt and pepper.
Place the turkey breast-side up on the indirect side of the grill with the legs facing the hotter side. Cover the grill and roast until almost done (an instant-read thermometer inserted in the thickest part of the thigh should register around 150 degrees F), 1 hour 30 minutes to 2 hours. Brush the turkey all over with the cranberry sauce. Cover the grill and continue cooking the turkey until a thermometer registers at least 165 degrees F in the thigh and 155 degrees F in the breast, 15 to 25 minutes more.
Let the turkey rest 30 minutes before carving. Serve with the reserved cranberry sauce on the side.
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