Food Network teaches how to crush, slice and mince garlic. Peel off some of the papery skin from the garlic and then smash the head of garlic with the heel of your hand to loosen the cloves; if you only need a few cloves, leave the head intact and pull some off. Separate the cloves. To peel a clove, cut away the root end with your knife. Lay the flat side of the knife over the clove while holding the knife handle, then with the heel of your free hand carefully whack the knife against the garlic to separate the skin from the clove. To crush the peeled garlic, lay the flat side of the knife over the clove and smash it again. To slice peeled garlic, lay the clove flat on the cutting board and hold it with the fingertips of one hand, keeping them curled under. Using a rocking motion with the knife, make thin slices by moving the knife slowly across the clove. To mince peeled garlic, lay the flat side of a knife over the clove and smash it. Roughly chop the clove then move your free hand flat across the tip of the knife and use a rocking motion to chop the garlic until it’s finely minced.
Make the rub: Whisk all the spice rub ingredients in a small bowl.
Make the bbq sauce: Heat the oil over medium-high heat in a heavy-bottomed medium saucepan. Add the onion and cook until soft, 3 to 4 minutes. Add the garlic and cook for 1 minute. Stir in 1/2 cup of the bourbon and cook until reduced. Add the ketchup and water, bring to a boil and simmer for 5 minutes. Stir in the remaining ingredients and simmer until thickened, stirring occasionally, about 10 minutes.
Cool for about 5 minutes, then transfer the mixture to a food processor and puree until smooth. Season with salt and pepper, to taste. Pour into a bowl, add the remaining 2 tablespoons of bourbon and allow to cool at room temperature. The sauce will keep for 1 week in the refrigerator stored in a tightly sealed container.
Heat the grill to medium heat. Brush the chicken with the 1/4 cup of oil and season on both sides with the spice rub. Season with salt and pepper, to taste. Grill the chicken slowly, with the lid closed, until golden brown on both sides and fat has rendered. Begin brushing the chicken liberally with the bbq sauce during the last 10 minutes of grilling.