In a small bowl whisk together the soy sauce, garlic, brown sugar, and sesame oil. In a medium sized skillet over medium high heat add the chicken and pour the sauce on top. Cook for about 3 minutes or until chicken is no longer pink.
Reserve 1/4 cup of chicken broth and cornstarch in a small bowl until cornstarch has dissolved. Add 1/2 cup chicken broth to the skillet with broccoli and cashews. Cover and cook for until broccoli is tender, about 3-5 minutes.
Add in the reserved broth and cornstarch mixture and continue to let simmer until the sauce has thickened. Serve with chopped green onions and serve over rice if desired.