Preheat the oven to 400°F (200°C). Lightly grease a 9x13-inch baking dish with a thin coat of oil.
Pat the chicken dry and season with a pinch of salt and pepper. Slice into bite-sized pieces so they cook quickly and evenly.
In a small bowl, whisk together the teriyaki sauce, honey (or maple syrup), vinegar, sesame oil, minced garlic, and grated ginger. This will be your glaze.
In the prep dish, spread the broccoli florets in an even layer. Scatter the chicken pieces over the broccoli.
Pour a portion of the teriyaki glaze over the chicken and broccoli, using just enough to coat without drowning everything. Reserve the rest for finishing the bake.
Toss to coat, then move the dish to the oven. Bake for 12–15 minutes, until the chicken is nearly cooked through and the broccoli is bright and tender-crisp.
Remove from the oven. Stir in the cornstarch slurry to thicken the glaze, then pour the remaining glaze over the top. Return to the oven for another 5–7 minutes, or until the sauce is glossy and the chicken is cooked through.
If you like a little extra glaze, broil for 1–2 minutes at the end, watching closely so nothing burns.
Let it rest for a couple of minutes before serving. This helps the flavors settle and the sauce to cling to the chicken and broccoli.