Combine soy sauce, brown sugar, honey, rice vinegar, grated ginger, minced garlic, and sesame oil in a small saucepan. Bring to a gentle simmer over medium heat.
Mix cornstarch with water to create a slurry, then whisk into the sauce. Cook for 2-3 minutes until thickened and glossy. Let cool slightly.
Cut chicken thighs into 1.5-inch cubes and place in a bowl. Pour half the cooled teriyaki sauce over chicken and toss to coat. Marinate for at least 30 minutes, up to 2 hours.
Soak wooden skewers in water for 30 minutes. Thread marinated chicken onto skewers, leaving small gaps between pieces for even cooking.
For grilling: Preheat grill to medium-high heat and oil grates. Cook skewers for 12-15 minutes, turning every 3-4 minutes and basting with reserved sauce during the last few minutes.
For oven: Set broiler to high. Place skewers on a foil-lined baking sheet with wire rack. Broil for 14-18 minutes, turning halfway and basting with reserved sauce near the end.
Cook until chicken reaches 165°F internal temperature and has caramelized edges. Garnish with sliced green onions and sesame seeds before serving.
