Chicken Yakitori

Name: Chicken Yakitori
Ingredients: 1 1/2 cups water; 1/4 cup kombu (1/2 ounce), broken into small pieces (see Note); 1/4 cup bonito flakes (see Note); 3 cups sake; 1 cup soy sauce; 3/4 cup mirin; 1/2 cup light brown sugar; 3 pounds skinless, boneless chicken thighs, cut into 1 1/2-inch pieces; 2 bunches scallions (about 12), cut into 1-inch lengths; One 4-inch piece of fresh ginger, peeled; Vegetable oil, for brushing