In a small bowl, whisk together the smoked paprika, garlic powder, dark brown sugar, ground cumin, chili powder, kosher salt, and black pepper to create the spice rub. Ensure there are no clumps of brown sugar remaining.

Pat the chicken pieces completely dry with paper towels to ensure crispy skin. Drizzle the olive oil evenly over the chicken, then generously massage the spice rub into all sides of the meat, getting the spices under the skin where possible.

Preheat your outdoor grill or indoor grill pan to medium heat, aiming for about 350°F to 375°F. Lightly oil the grill grates with a high-smoke-point oil to prevent the chicken from sticking during cooking.

Place the chicken on the grill, skin-side down. Cook for 15 to 20 minutes with the lid closed, turning every 5 minutes, until the skin is deeply browned and rendered.

Reduce the grill heat to medium-low to prevent the sugars from burning. Brush the chicken generously with the hickory smoke BBQ sauce and continue cooking for another 10 to 15 minutes, turning and basting frequently, until a meat thermometer inserted into the thickest part reads 165°F.

Remove the chicken from the grill and transfer it to a clean serving platter. Let the chicken rest for 5 to 10 minutes before serving, which allows the juices to redistribute for perfectly tender meat alongside your favorite potato salad.