Combine soy sauce, mirin, saké and sugar in a small saucepan and bring to boil over medium high heat. Reduce heat to simmer and cook 8–10 minutes, stirring occasionally, until the alcohol has evaporated and glaze has thickened enough to lightly coat a spoon.
In a large bowl, season chicken pieces with one teaspoon salt and a few dashes of white pepper. Toss to combine.
Cut white and pale-green portions of scallions into 1-inch pieces. Place in a small bowl with vegetable oil and toss to combine.
Thread each skewer tightly with alternating pieces of chicken and scallion.
Oil grill. Place skewers of chicken over the hottest portion of the grill. Turn every 2 minutes, lightly seasoning with additional salt and white pepper, until chicken is lightly browned and nearly cooked through, about 8–9 minutes.
Lightly season with additional salt and white pepper, to taste. Baste each skewer with glaze and sear briefly, allowing glaze to caramelize before removing from grill. Drizzle with additional glaze. For an added boost of flavor, sprinkle with shichimi togarashi or sansho powder. Serves 4–6 as a side dish.