01 - In a large mixing bowl, combine the barbecue sauce, olive oil, apple cider vinegar, brown sugar, smoked paprika, garlic powder, onion powder, kosher salt, and black pepper. Whisk until smooth and fully incorporated.
02 - Measure out 1/4 cup of the marinade mixture and set aside in a separate container for basting during grilling.
03 - Add the chicken thighs and drumsticks to the bowl with the remaining marinade, turning each piece to coat thoroughly. Cover tightly with plastic wrap and refrigerate for at least 1 hour, or up to overnight for more pronounced flavor.
04 - Preheat an outdoor grill to medium-high heat, approximately 375°F to 400°F. Lightly oil the grill grates using a folded paper towel dipped in vegetable oil to prevent sticking.
05 - Remove the chicken from the marinade, allowing any excess to drip off. Place the pieces skin-side down on the grill and cook for 6 to 8 minutes per side, brushing with the reserved basting sauce and turning occasionally, until the skin is deeply charred and the internal temperature reaches 165°F when tested with a meat thermometer.
06 - Transfer the grilled chicken to a platter and allow it to rest for 5 minutes so the juices redistribute. Garnish with chopped fresh parsley if desired and serve immediately.