You can prepare the tare sauce (marinade) a day or two ahead of time. Let it cool to room temperature and refrigerate until you’re ready to marinate the chicken.
Pat the chicken dry and cut it into 1½-inch pieces. Place it in a shallow bowl. Sprinkle with salt and pepper, rubbing to coat. Refrigerate while making the marinade.
Tare Sauce
Combine soy sauce, mirin, sake, water, brown sugar, sesame oil, garlic, and ginger in a small saucepan. Bring to a boil. Cook 15 minutes or until thick enough to coat the back of a spoon. Cool to room temperature.
Set aside 1/3 cup of the marinade. Pour the remaining marinade over the chicken, tossing to coat. Cover and refrigerate for 2 hours.
To Finish
Soak 8-10 wooden skewers 30 minutes.
Cut the white and pale-green parts of onions into 1-inch pieces. Thinly slice darker green parts for garnish.
Preheat the grill to high.
While the grill heats up, remove the chicken from the marinade; discard the marinade. Thread the chicken, alternating with 1-inch green onion pieces, snugly onto the skewers.
Oil the grill grates. Grill skewers 5-7 minutes or until done, turning to cook evenly and basting with the reserved tare sauce. Serve garnished with thinly sliced green onions and, if desired, sesame seeds.