Heat one tablespoon oil in a sauté pan over medium heat. Add chicken and sauté for about six minutes, or until cooked through. Remove chicken from pan and set aside.
In a separate bowl, combine garlic, ginger, soy sauce, teriyaki sauce, and honey.
Heat remaining tablespoon oil in the same pan. Add broccoli. Cook for a few minutes, until broccoli is defrosted. Add sauce and chicken, and cook for an additional five minutes. Add cashews and cook for an additional two minutes.
Using a slotted spoon, remove chicken, broccoli, and cashews from pan and place on serving dish. Add cornstarch mixture to the remaining sauce. Cook until sauce is thickened, stirring constantly. Pour thickened sauce over chicken and serve.