Place the chicken pieces in a large bowl, or a ziplock bag. Season with salt and pepper. (I used ½ teaspoon salt and ¼ teaspoon pepper.) Set aside.
Add all of the ingredients for the marinade to a bowl, and whisk until well incorporated. Reserve ½ cup of the marinade (to use for the sauce).
Add the remaining marinade to the chicken and mix well. Cover, and allow to marinate in the refrigerator for 1 hour, or up to one day. (Keep the reserved marinade refrigerated as well.)
To a large bowl, add all of the vegetables: bell peppers, onion, zucchini. Toss with the 2 tablespoons of olive oil and ½ teaspoon salt and ¼ teaspoon pepper.
Preheat the oven to 450ºF.
Line a large baking sheet with foil and lightly grease with cooking spray.
Arrange the vegetables in one layer on the baking sheet. Top with the chicken pieces (discarding any excess marinade, see notes).
Bake about 15 minutes, or until chicken is cooked through. Toss about halfway during baking time.
Meanwhile, add the reserved marinade to a sauce pan. Mix the cornstarch and ¼ cup water in a cup, then add it to the saucepan.
Bring the sauce to a simmer over medium heat. Reduce heat to medium-low and simmer for about 3-5 minutes, or until slightly thickened, occasionally stirring. Cover, and set aside.
Once the chicken/veggies are done, broil on High for about 1-2 minutes, 6" from the heat source. (Watch carefully so that it doesn't burn! You just want to get a bit of browning. Mine took a little less than 2 minutes.)
Remove from the oven, and drizzle the sauce over the top of the chicken and veggies.
Optional: Garnish with sesame seeds and/or chopped cilantro. Serve alone, or with a side of rice.