Preheat the oven to 500°. In a saucepan, combine the soy sauce, mirin, sake, vinegar, brown sugar and ginger. Add the cornstarch mixture and bring to a boil over high heat. Cook, stirring, until glossy and slightly thickened (about 3 minutes). Put sauce to a bowl.
Set the turkey in a large roasting pan and scatter the onions around it. Season the turkey inside and out with salt and white pepper. In a small bowl, blend 4 tablespoons of the butter with the olive oil and brush some over the turkey.
Roast the turkey for 30 minutes, or until golden in color. Baste with the butter mixture and add the cup of water to the roasting pan. Reduce the oven temperature to 325° and roast the turkey for 1 hour, basting twice with the remaining butter mixture; loosely cover the bird with foil if the breast browns too quickly.
Pour half of the teriyaki sauce into a bowl; baste the turkey with it. Roast the turkey for 1 1/2 hours longer, basting with the sauce from the bowl every 30 minutes; the turkey is done when the skin is completely lacquered and a thermometer inserted in an inner thigh reads 170°. Transfer to a carving board; let rest for 45 minutes.
Meanwhile, strain the pan juices into a bowl; skim off the fat and save the onions. Set the pan over 1 burner. Add the onions to the pan and cook over high heat, stirring, until browned, about 3 minutes. Add the pan juices, chicken stock and the left over teriyaki sauce. Bring to a boil, scraping up any browned bits from the bottom of the pan.