Preheat the oven to 375°F.

Line a large baking sheet with parchment paper. Arrange the chicken and broccoli florets on the baking sheet and drizzle with sesame oil. Toss with a rubber spatula to coat.

Bake the chicken and broccoli on middle rack of oven for 15 minutes. While chicken and broccoli bake, prepare the sauce.

Whisk together the water and cornstarch in a small saucepan until smooth. Add the soy sauce, brown sugar, rice vinegar, sesame oil, garlic, and ginger root. Whisk to combine.

Set the pan over medium heat and bring the sauce to a low boil, whisking regularly. Once bubbling, whisk the sauce steadily until it begins to thicken slightly, 1-2 minutes. Remove pan from the heat and set aside.

Open the oven and remove the baking sheet. Pour the sauce evenly over the chicken and broccoli. Toss with a rubber spatula to coat, and sprinkle with the sesame seeds. Return baking sheet to oven and continue baking the chicken and broccoli until chicken is cooked through and broccoli is fork-tender, 10-12 minutes.

Check to see that the dish is done. Remove from oven or add time as needed.

Transfer the chicken and broccoli to serving dishes and top with the finely chopped scallions. Serve immediately.