Begin by laying the chicken thighs or drumsticks on a baking sheet, ensuring they have some space between each piece. Allow them to come to room temperature for about 30 minutes while you prepare other ingredients. Pat the chicken dry with paper towels.

In a small mixing bowl, combine the kosher salt, garlic powder, smoked paprika, chili powder, onion powder, and black pepper. Mix thoroughly and coat each piece of chicken with the dry rub.

Prepare your grill for cooking by setting one side to high heat for direct grilling and leaving the other side off for indirect cooking. Preheat the grill to around 400°F (204°C).

Carefully place the seasoned chicken on the side of the grill set for indirect heat. Cover the grill and cook the chicken for approximately 30-35 minutes, flipping every 10 minutes until an internal temperature of 160°F (71°C) is reached.

In the last 6-8 minutes of cooking, brush the homemade BBQ sauce over the chicken, flipping each piece and basting with more sauce to create a glaze, targeting an internal temperature of 170°F (77°C).

Once the desired temperature is reached, transfer the BBQ chicken to a serving platter, allow it to rest for a couple of minutes, and serve with extra BBQ sauce on the side.