Make the marinade: In a bowl, whisk soy sauce, mirin, honey, rice vinegar, garlic, ginger, and sesame oil. Taste and adjust sweetness or saltiness as needed.

Marinate the drumsticks: Pat the chicken dry. Add to a large zip-top bag or bowl and pour in two-thirds of the marinade. Reserve the remaining third for the glaze. Marinate for at least 1 hour (up to overnight) in the fridge.

Preheat the grill: Heat to medium (about 375–400°F). Clean and oil the grates to prevent sticking.

Start grilling: Shake off excess marinade and place drumsticks on the grill. Cook covered for 20–25 minutes, turning every 5 minutes to prevent burning and to cook evenly.

Make the glaze: While the chicken grills, pour the reserved marinade into a small saucepan. Bring to a simmer. Stir cornstarch with water to make a slurry, then whisk it into the sauce. Simmer 1–2 minutes until thick and glossy.

Glaze and finish: During the last 5 minutes of grilling, brush the drumsticks with the thickened teriyaki glaze, turning and brushing again to build a sticky coating.

Check doneness: Use an instant-read thermometer. You want 175–185°F at the thickest part for tender, juicy dark meat.

Rest and serve: Let the chicken rest 5 minutes. Sprinkle with sesame seeds and green onions. Add lime wedges if you like a bright finish.