Heat 1 teaspoon oil in a large pan over medium-high heat. Add the onion and cook for 3-4 minutes or until softened and lightly browned.
Add the broccoli and 1 tablespoon of water. Cook, stirring occasionally, until broccoli is tender, approximately 3 minutes.
Add the bell pepper and ginger and cook for 2 minutes more, or until peppers are just softened.
Season the vegetables with salt and pepper to taste, then transfer to a plate. Cover to keep warm.
Wipe out the pan with a paper towel and add the remaining 2 teaspoons of oil. Add the chicken and season with salt and pepper to taste. Cook for 3-4 minutes on each side, or until chicken is browned and cooked through. Add the vegetables back to the pan.
While the chicken is cooking, make the sauce.
In a small bowl mix together the soy sauce, honey, and chili garlic sauce. In another small bowl, add the cornstarch along with 2 teaspoons of cold water, whisk to combine.
Add the cornstarch mixture to the soy sauce mixture and stir until thoroughly combined
Pour the sauce into the pan with the chicken and vegetables and turn up the heat to high. Bring the sauce to a boil and cook for 30 seconds or until just thickened.
Sprinkle the cashews and green onions over the top and serve, with brown rice if desired.