Prepare a brine by pouring the water, kosher salt and brown sugar into a vessel large enough for the number of legs you plan to cook.
Make sure that the salt and sugar have completely dissolved before adding the legs.
Adjust the ingredients based on how many legs you are fixing-shoot for just enough to fully cover the drumsticks.
Feel free to use something like a bowl or a plate in order to keep the legs below the water level of the brine.
Refrigerate the legs for anywhere between 4 and 24 hours.
Remove them from the fridge 1 hour before you want to cook them, in order to bring them up to room temperature.
Remove the legs from the brine and pat them dry.
Right before you cook them, drizzle olive oil over each leg and rub in a mixture of salt and black pepper.
Prepare your grill for indirect heating.
Feel free to add some smoking wood for extra aroma.
Prepare a basting mix of honey, vinegar, BBQ sauce and Worcestershire sauce and combine them all until it forms an even consistency.
You can do this up to a day ahead of when you plan to cook the legs, storing it in the fridge until it is time to use it.
Begin grilling the legs with the grill’s lid as closed as you can have it.
Begin basting with the mix from the previous step on a frequent, regular basis so that the legs become covered in a rich, dark glaze of caramelization.
Turn the legs every so often, continuing to baste.
Make sure that you keep the lid closed between basting sessions in order to keep as much heat and smoke trapped within as possible.
While individual cooking times can vary, most legs only need 20-30 minutes of indirect heat, at a moderate temperature, to be done.
Cooking on high temperatures may finish the legs quicker, but also increases the risk of burning the legs.
Check for doneness by either using a meat thermometer or making a cut into one leg.
The good news is that brining mitigates most of the risk of overcooking while also keeping the legs nice and moist.
Once the legs are done, take them off the grill and onto a serving dish.
Cover with foil and allow them to rest for 10-15 minutes.