Pat the drumsticks dry with paper towels. This helps the glaze stick and the skin crisp a bit as it cooks.
In a bowl, whisk together soy sauce, mirin, honey, rice vinegar, garlic, and ginger. If you’re avoiding sweetness, reduce the honey to 1 tablespoon and adjust to taste.
Heat a large skillet over medium-high heat. Add a light coating of oil if your pan isn’t nonstick. Sear the drumsticks in batches, turning once, until they’re light golden on the outside—about 3 to 4 minutes per side. You don’t need to cook them through here; you’re just building flavor and color.
Return all the drumsticks to the pan. Pour in the teriyaki sauce. Bring to a simmer and cook for about 6 to 8 minutes, turning occasionally so each piece gets coated.
Stir the cornstarch slurry (1 tablespoon cornstarch mixed with 1 tablespoon water) and pour into the pan. Cook, stirring, until the sauce thickens to a glossy glaze and the chicken reaches an internal temperature of 165°F (74°C). If the sauce thickens too quickly, add a splash more water.
Taste and adjust. A little more honey can balance saltiness, or a splash more soy can deepen the glaze. If you like a shinier look, you can finish with a few drops of sesame oil.
Remove from heat. Sprinkle with sesame seeds and scallions if using. Let the meat rest a minute, then serve.