For the BBQ sauce: Heat the oil in a medium saucepan over medium heat. Add the onion, sprinkle with salt and pepper and cook until soft, 5 minutes. Add the garlic, chili powder and smoked paprika. Cook 1 minute. Add the beer or water. Stir in the ketchup, vinegar, Worcestershire, brown sugar and molasses.
Bring to a low boil and reduce the heat to low. Cover and simmer for 35 minutes, stirring occasionally.
For the chicken: Meanwhile, preheat your grill to medium heat. Spatchcock or flatten the chicken by removing the backbone. To remove the backbone, flip the chicken over so that it sits breast side down and use a pair of kitchen shears to carefully cut along either side of the backbone. Flip the chicken over and press down to flatten.
Combine the chili powder, garlic powder, onion powder, smoked paprika and kosher salt in a small bowl. Rub the oil over both sides of the chicken and sprinkle the spice mix evenly over the skin and meat.
Place the chicken bone side down onto the grill, close the lid and cook for 30 minutes.
Transfer about half of the BBQ sauce into a small bowl and begin basting the top of the chicken every 5 minutes or so and continue to cook until the internal temperature of the thickest part of the thigh reaches 165 degrees F (75 degrees C), 15 to 20 minutes.
Remove the chicken from the grill, cover it loosely with a piece of aluminum foil and allow it to rest for 10 minutes before serving with the reserved BBQ sauce.
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