Make the teriyaki sauce by combining all ingredients but the cornstarch and 2 tablespoons water in a small saucepan on medium-high heat. In a small bowl, stir together cornstarch and 2 tablespoons water until cornstarch is dissolved, then add to saucepan. Bring to a boil and simmer until thickened, around 5 minutes.
Chop carrots into small pieces and chop green beans into bite size pieces. Saute for 5 minutes until crisp tender. Cut chicken into thin strips or bite size pieces.
Preheat oven to 375* F and spray a 9x13 baking dish with non-stick spray. Spread veggies along the bottom of the dish, followed by the chicken. Spread rice on top. Pour 1 cup of chicken broth over everything, and then spread 1 cup of teriyaki sauce on top, making sure to cover well.
Cover dish in foil and bake for 40 minutes. Remove foil and stir just a bit to make sure everything is cooking evenly, and add 1/2 cup more chicken broth if too dry. Then put back in the oven (keeping the foil off) for 10-15 minutes, until chicken and veggies are cooked. Pour remaining teriyaki sauce on top, to taste.