Make the BBQ sauce: Whisk together all ingredients in a small bowl and set aside for later use.
Heat your barbecue to low heat.
Sprinkle drumsticks with salt and pepper and baste with olive oil on all sides.
Once your grill is hot, place the drumsticks on the grill. The key to these drumsticks is low and slow. Turn your drumsticks every 3-4 minutes. Continue this process until the drumsticks begin to brown and are cooked through. The internal temperature should be between 165-175 degrees. Baste the drumsticks with the bbq sauce during the last few turns.
Remove drumsticks from grill and transfer to a plate. Sprinkle with chopped green onion. Enjoy!