Add the cornstarch and half the chicken broth to a small mixing bowl, then whisk to combine. Add the remaining ingredients, stir to combine and set aside.
FOR THE VEGETABLES:
Add a couple inches of water into a medium-sized pot, then place a steamer basket inside. Add the broccoli, sugar snap peas, bell pepper strips, shredded carrots to the basket, then turn the heat to high. Once the water is boiling, place a lid on top, turn the heat down to low and steam until the broccoli is tender, 5-7 minutes. Set aside.
FOR THE STIR FRY:
In a large skillet, heat the sesame oil over high heat just until hot — do not burn the sesame oil. Once hot, add the chicken and spread into an even layer in the bottom of the skillet. Season with salt and pepper, then let the chicken sit and sear undisturbed until golden brown on the bottom, 1-2 minutes. Stir fry until the chicken is nearly cooked through, 2-3 more minutes.
Turn the heat down slightly, then give the stir fry sauce another stir to ensure the cornstarch has not settled into the bottom of the bowl. Pour the sauce into the pan, then stir with a spatula until the sauce has slightly thickened and reduced, 1-2 minutes, turning the heat down if necessary.
Add steamed vegetables to the pan and cook 1-2 minutes.