Preheat the oven to 425°F (220°C) and line a sheet pan with parchment for easy cleanup.
In a small bowl, whisk together the soy sauce, honey, rice vinegar, minced garlic, and grated ginger to make the glaze.
In a separate bowl, toss the chicken pieces with a pinch of salt and pepper and the cornstarch until lightly coated. This helps the sauce cling to the chicken.
Spread the chicken pieces on the sheet pan in a single layer. Drizzle with a teaspoon of sesame oil and bake for about 8–10 minutes.
Meanwhile, toss the broccoli with a little oil and a pinch of salt. After the chicken has started cooking, scatter the broccoli on the pan beside the chicken.
Pour the glaze over the chicken and broccoli. Return to the oven and bake for another 6–10 minutes, until the chicken is cooked through and the broccoli is tender-crisp.
In a small cup, whisk the remaining cornstarch with water to make a slurry. If the pan juices are thin, stir the slurry into the pan and bake for 1–2 minutes more to thicken.
Remove the sheet pan from the oven. Give everything a gentle toss to coat in the glossy glaze. Sprinkle with sesame seeds and serve hot.