Remove the chicken thighs from the refrigerator, place on a parchment-lined baking sheet, and pat dry.
In a small bowl, combine the rub ingredients: brown sugar, salt, smoked paprika, garlic powder, onion powder chili powder, cumin, black pepper, cloves, and cayenne.
Rub all over the chicken, working some of the rub underneath the skin. Let sit for 30 minutes at room temperature while you prepare the smoker.
Heat your smoker to 225°F. Prior to lighting, add the wood, mixing it with the charcoal. It’s OK if your smoker gets a bit hotter than 225°F; just note that the chicken will cook more quickly. Do not cook it any lower than 225°F or the skin will be rubbery.
Add the chicken thighs skin-side up and smoke until they reach 165°F on an instant-read thermometer inserted at the thickest part, 45 minutes to 1 hour 15 minutes depending upon the size of your thighs, your smoker set up, and how much your smoker temperature is fluctuating. Smoke to temperature, not to time on the clock.
While the chicken is smoking, heat together the barbecue sauce and butter, stirring until the butter melts completely. Once the chicken reaches around 150°F (about 40 minutes in), baste the chicken all over with the sauce, then continue smoking until the chicken reaches 165°F.
Remove the chicken from the smoker. Tent with foil and let rest 10 minutes. If you'd like to crisp the skin, place the chicken under the oven broiler for a few minutes just before serving.
Notes
TO STORE: Store leftover smoked chicken thighs in an airtight container in the refrigerator for up to 3 days.
TO REHEAT: Loosely cover the chicken thighs with foil and reheat in a 350°F oven until warmed through, or warm carefully in the microwave.
TO FREEZE: Store smoked chicken thighs for up to 2 months in the freezer. Wrap them well and place them in an airtight container or freezer bag. Thaw the smoked chicken thighs overnight in the refrigerator before reheating according to the instructions above.