Combine all of the ingredients for the brine in a large pot and bring to a boil. Let cool. if you're short on time, you can also start by boiling the brine with just 2 quarts of water and then adding ice to cool to 1 gallon of brine.
While that's happening, rinse your turkey legs and set aside in a large container (one that will fit into your refrigerator). You may want to use two separate containers. When the brine has cooled, pour the brine over the turkey legs, making sure they are totally submerged. Cover and refrigerate overnight.
If you want to expedite the process, use a marinade injector, injecting one syringe-full of brine into each turkey leg (1½ syringe-fulls for the larger turkey legs). Then, let brine as usual for 5-6 hours. This way, the turkey legs don't need to brine overnight. Sounds gruesome, but it really expedites the process, and these marinade injectors are pretty inexpensive!
When the turkey legs are ready, heat your charcoal. Your key tools for this recipe are a charcoal grill, a chimney starter, charcoal, and wet wood chips, which provides the smoky flavor. Fill your chimney with charcoal and light the coals with a piece of newspaper. Let heat for a solid 15-20 minutes or so--until the coals are slightly white hot. Also, take 1-2 handfuls of wood chips and soak them in water while the coals are heating.
Pour the coals into the grill and scatter the wood chips around the coals. Lay your grill rack over the coals. Place the turkey legs on the grill rack and close the grill.
chimney-full of coal is enough to start for an average-sized charcoal grill. Add another chimney of coal every 20-30 minutes, depending on the kind of charcoal you're using. Periodically add additional wet wood chips to make more smoke as needed. More wood chips makes more smoke, increasing the "hammy" smoked flavor of the turkey legs. You can cater this to your personal preferences. I like a very hammy smoked turkey leg; my aunt prefers more of a natural flavor. Take your pick!
The slow cooking method is key here. Periodically check the turkey legs, turning every once in a while, and make sure the grill maintains a temperature of 300-325 degrees. There is some element of trial and error to this if you're a first-timer; make observations and adjust amounts of charcoal, wood chips, and heat over the course of the cooking time.
Maintain the grill, charcoal, and wood chips, letting the turkey cook for 3 ½ to 4 hours--until the turkey legs have a nice, dark smoky color that a young Chinese girl once thought only existed within the walls of Disney World.
Serve immediately and let your inner caveman / inner Disney World fanatic dig in!