Preheat the oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish with non-stick spray or a little oil.

Make the cornstarch slurry.

In a small bowl, mix the cornstarch with 2 tablespoons of water until completely smooth. Set aside.

Start the teriyaki sauce.

In a small saucepan over medium heat, combine the soy sauce, honey or brown sugar, rice vinegar, sesame oil, minced garlic, and grated ginger. Bring the mixture to a gentle simmer.

Thicken the sauce.

Slowly whisk the cornstarch slurry into the simmering sauce. Continue cooking and stirring for 2 to 3 minutes, or until the sauce thickens. Remove from heat.

Combine the casserole filling.

In a large mixing bowl, combine the cooked rice, cooked chicken, broccoli florets, diced red bell pepper, shredded carrots, and half of the sliced green onions.

Add the sauce.

Pour about ¾ of the thickened teriyaki sauce over the rice and chicken mixture. Gently stir until everything is evenly coated.

Transfer to the baking dish.

Spread the mixture evenly into the prepared 9x13-inch baking dish. Drizzle the remaining teriyaki sauce over the top.

Bake covered.

Cover the baking dish tightly with aluminum foil and bake for 20 minutes.

Finish baking uncovered.

Remove the foil and bake for another 5 to 10 minutes, or until the casserole is heated through and slightly golden and bubbly on top.

Garnish and serve.

Remove from the oven. Sprinkle with sesame seeds and the remaining sliced green onions before serving warm.