Make the brine. In a large food-safe container, combine cold water, kosher salt, brown sugar, black peppercorns, smashed garlic cloves, bay leaves, smoked paprika, onion powder, and optional curing salt. Stir until the salt and sugar are dissolved.
Brine the turkey legs. Add the turkey legs to the brine, making sure they are fully submerged. Cover and refrigerate for 8 to 12 hours.
Remove and dry. Take the turkey legs out of the brine and discard the brine. Pat the turkey legs very dry with paper towels.
Air dry the skin. Place the turkey legs on a wire rack over a sheet pan and refrigerate uncovered for 1 to 2 hours if time allows. This helps the skin dry so it can color better in the smoker and crisp better on the grill.
Season the turkey legs. Lightly coat the turkey legs with olive oil, melted butter, or yellow mustard. Mix the BBQ rub ingredients together and season the turkey legs evenly on all sides.
Preheat the smoker. Set the smoker to 275°F using apple, cherry, pecan, hickory, or oak wood.
Start smoking. Place the turkey legs directly on the smoker grates. Insert a leave-in meat probe into the thickest part of one turkey leg without touching the bone.
Smoke until almost done. Smoke the turkey legs for about 2 to 2 1/2 hours, or until the skin is deep golden brown to reddish mahogany and the internal temperature reaches about 160°F to 165°F.
Preheat the grill. While the turkey legs are finishing in the smoker, preheat a charcoal grill, gas grill, or grill grates to 400°F to 450°F for direct heat.
Make the butter baste. In a small bowl, mix melted butter, honey, BBQ sauce, and optional hot sauce.
Grill finish the turkey legs. Move the smoked turkey legs to the hot grill grates. Grill for 8 to 15 minutes, turning every 2 to 3 minutes, until the skin tightens, lightly crisps, and gets charred in spots.
Baste during the grill finish. Brush the turkey legs lightly with the butter baste during the last few minutes of grilling. Do not baste too early over direct heat or the sugars can burn.
Cook to final temperature. Continue grilling until the turkey legs reach 175°F to 185°F internal in the thickest part of the meat. Turkey is safe at 165°F, but dark meat eats better in the higher range.
Rest the turkey legs. Remove the turkey legs from the grill and rest for 10 to 15 minutes before serving.
Serve fair-style. Serve whole with butcher paper wrapped around the bone, or slice the meat off the bone for sandwiches, bowls, mac and cheese toppers, or loaded baked potatoes.