Soak the bamboo skewers in water for 30 minutes, or at least 10 minutes if you are short on time.

Separate the dark green tops from the white and light green parts of the negi. Cut the white and light green parts into 1 1/4-inch pieces and halve the dark green tops crosswise.

In a small saucepan, combine the soy sauce, mirin, sake, water, brown sugar, and green negi tops. Bring to a boil over high heat, then lower the heat and simmer uncovered until the mixture reduces to about one-third of its volume, about 30 minutes.

Let the tare cool to room temperature, then reserve about one-third of the sauce for final basting.

Cut the chicken thighs into 1 1/4-inch squares, fold each piece in half, pierce the folded edge at a 45-degree angle, and thread onto the skewer with a piece of negi.

Each skewer should hold about 3 chicken pieces and 2 negi pieces.

Line a baking sheet with foil, place an oven-safe wire rack on top, and grease the rack with neutral oil.

Lay the skewers in two rows on the rack, cover the exposed ends with folded foil strips. Heat the broiler to High (550°F), with the rack in the middle position about 8 inches from the heat.

Preheat for 3 to 5 minutes, then broil for 6 minutes. Baste, flip, and broil for a few minutes more until the chicken reaches 165°F and looks glossy.