Heat the 1 tablespoon olive oil over medium-high heat in a large wok or skillet. Add the 1 pound boneless skinless chicken breast, and cook, tossing frequently until mostly cooked through.
Add the 1 diced zucchini, 1 chopped red bell pepper, 1 cup sliced mushrooms, ½ cup shredded carrots, and 1 cup snow peas to the pan, and cook until the vegetables are tender and the chicken is no longer pink. Add 1 cup whole cashews.
Pour the ¾ cup chicken broth, ¼ cup low sodium soy sauce, 3 cloves minced garlic, 1 tablespoon brown sugar, and 1 teaspoon sesame oil over the chicken and vegetables.
In a small bowl whisk together 1 tablespoon cornstarch and 2 tablespoons water to make a slurry. Pour the slurry into the pan and stir until incorporated. Simmer for 2 minutes or until the sauce has thickened.
Garnish with sliced green onions and serve over rice if desired.