01 - In a large mixing bowl, combine the barbecue sauce, olive oil, apple cider vinegar, brown sugar, smoked paprika, garlic powder, onion powder, salt, and black pepper. Whisk until smooth and well blended.
02 - Measure out 1/4 cup of the marinade mixture and set aside in a small bowl for basting during grilling.
03 - Add the chicken thighs and drumsticks to the remaining marinade, turning to coat each piece thoroughly. Cover the bowl 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. Cook for 6 to 8 minutes per side, turning occasionally and brushing with the reserved basting sauce, until the skin is charred and the internal temperature reaches 165°F at the thickest part.
06 - Transfer the grilled chicken to a platter and let rest for 5 minutes to allow the juices to redistribute. Garnish with chopped fresh parsley if desired and serve immediately.