For Brine: In a large Dutch Oven or pot combine brine ingredients. Stir for 1-2 minutes to dissolve salt and sugar. Immerse turkey legs in brine, cover, refrigerate for 24 hours.
Remove turkey legs from brine, rinse under cold water and pat dry. Discard brine.
Preheat BBQ grill* to medium (375ºF – 400ºF), using indirect heat (one side of the grill is off).
In a small bowl mix all Dry Rub ingredients. Massage rub all over turkey legs to completely cover.
Over the DIRECT heat, sear legs for 2-3 minutes on all sides. Remove to the INDIRECT side of grill and cook, with lid down, for 25 minutes.
Prepare Honey Garlic Sauce: Combine Honey Garlic Sauce ingredients, except cornstarch and water, in as sauce pan. Combine cornstarch with water in a small dish, then add to sauce pan. Bring to boil, reduce heat and simmer for 2-4 minutes on low until thickened. Set aside.
After 25 minutes, open BBQ lid and brush legs with Honey Garlic Sauce. Close lid and continue to cook until legs reach an internal temperature of 180ºF (about 15 to 20 minutes). Liberally brush with remaining Honey Garlic Sauce and serve.