Pat the drumsticks dry and season lightly with a pinch of salt. This helps the skin crisp and the glaze cling to the meat.
Preheat your oven to 425°F (220°C). If you prefer, you can use a grill or a skillet on medium-high heat, but the oven gives you a beautifully even glaze.
In a large bowl, toss the drumsticks with the olive oil to coat. If using, you can also rub a tiny amount of minced garlic onto the skin for extra aroma.
Spread the drumsticks on a baking sheet lined with parchment paper or a lightly greased rack. Bake for 25–30 minutes, turning once halfway through, until the skin is deeply golden and the internal temperature reaches 165°F (74°C).
Meanwhile, prepare the glaze. In a small saucepan, combine soy sauce, mirin, brown sugar, rice vinegar, garlic, and ginger. Bring to a gentle simmer over medium heat.
Whisk the cornstarch slurry into the simmering sauce and cook 1–2 minutes more, until the glaze thickens to a glossy consistency that coats the back of a spoon.
When the drumsticks are nearly cooked, reserve a small amount of glaze for brushing. Brush the hot drumsticks with the thickened glaze, then return to the oven for 3–5 minutes to set the glaze. Repeat once if you want a deeper lacquer.
Remove from heat, drizzle with any remaining glaze, and garnish with sesame seeds and sliced green onions if using. Let rest a couple of minutes before serving.