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.
Arrange on a serving platter and serve.