Heat the oven to 375°F and lightly grease a 9x13-inch baking dish.

Cut the chicken into roughly ¾- to 1-inch pieces.

Add the soy sauce, ½ cup water, brown sugar, rice vinegar, ginger, garlic, and sesame oil to a small saucepan. Bring to a gentle simmer over medium heat.

Stir the cornstarch with 2 tablespoons cold water until smooth. Slowly whisk it into the simmering sauce.

Cook for 1 to 2 minutes, stirring, until the sauce becomes glossy and lightly thickened. Remove from the heat.

Heat the oil in a large skillet over medium-high heat. Add the chicken in a fairly even layer and cook for about 5 to 6 minutes, turning occasionally, until lightly browned and mostly cooked through.

In a large bowl, combine the cooked rice, broccoli, carrots, chicken, and about three-quarters of the teriyaki sauce. Fold gently until evenly coated.

Transfer to the prepared baking dish and spread into an even layer. Spoon the remaining sauce over the top.

Cover with foil and bake for 20 minutes.

Remove the foil and continue baking for 5 to 8 minutes, or until the casserole is hot throughout and the thickest pieces of chicken reach 165°F.

Rest for 5 minutes before serving. Finish with sliced green onions and sesame seeds if desired.