In a large pan over high heat, heat vegetable oil. Add garlic, broccoli, and bell pepper. Cook until soft, 5 minutes. Add chicken and cook until golden and cooked through, 8 minutes. Stir in cashews and season with pepper.
In a small bowl, whisk together soy sauce, honey, and sesame oil. Pour into pan and let simmer until thickened, 5 minutes.
