Whisk together 1/4 cup of the brown sugar, 1/4 cup of the soy sauce, 2 tablespoons of the sake, and 4 cloves of the chopped garlic. Place the chicken in a casserole dish and cover with the sugar-soy marinade. Cover and refrigerate for at least 2 hours, and up to 24.

In a saucepan, combine the remaining 1/2 cup brown sugar, 1/2 cup soy sauce, 1/4 cup sake, 2 cloves of chopped garlic, with the pineapple juice and vinegar. Bring to a boil over medium-high heat. Reduce heat to low, and simmer, stirring occasionally, for 12-15 minutes, until the sauce reduces to 1 1/4 cups. Whisk in the cornstarch slurry, and cook 1 more minute, until the sauce thickens. Transfer the sauce to two small bowls, dividing evenly. Set aside.

Heat a gas or charcoal grill to medium (about 350-450˚F.) Remove chicken from refrigerator and let sit at room temperature for 15 minutes. When the grill is hot, use a towel dipped in vegetable oil to lightly grease the grate. Place the chicken on the grill, skin-side down, cover, and cook about 5 minutes, until it has grill marks. Flip, cover, and cook another 5 minutes on the other side. Flip once more, then use a brush to generously coat the chicken with sauce from one of the bowls (leave the second bowl for serving at the table). Cook 5 minutes, flip and brush the other side with sauce. Continue to flip and brush with sauce until a thermometer inserted into the thickest piece reads 160-165˚F, and the meat near the bone is no longer pink. It will be 25-30 minutes total cooking time.