In a small saucepan, whisk together all sauce ingredients over medium high heat until sauce thickens (about 10 minutes). Set aside.
Place chicken breasts in an 8 x 11 baking dish. Pour sauce over chicken, reserving 2 Tablespoons.
Bake 35 minutes until chicken is cooked through. Remove from oven and shred chicken.
Add vegetables, edamame, and rice to the dish. Stir until fully combined. Drizzle remaining 2 Tablespoons teriyaki sauce over the casserole, and bake another 15 minutes.