Combine the sauce ingredients in a large, heavy pan. Simmer over medium heat until reduced by about one-third, 15 to 20 minutes. The sauce can be made a day or two ahead.
Prepare the smoker for barbecuing, bringing the temperature to 200°F to 220°F. Grease a large smoke-proof baking pan or dish.
With a cleaver or butcher knife, remove the chicken wing