In a medium bowl, add chicken broth, soy sauce, brown sugar, toasted sesame seed oil, cornstarch, garlic and ginger. Whisk and set aside.
Preheat large non-stick skillet on medium-high heat and add 1 tablespoon of oil. Add chicken, sprinkle with salt and pepper, and cook for 5-7 minutes, stirring just a few times and allowing brown edges to form. Transfer to a large plate and set aside.
Return skillet to medium-high heat, add remaining 1 tablespoon of oil, onion, bell peppers and garlic. Cook for 3 minutes, stirring just a few times and allowing to brown.
Reduce heat to low-medium and add cabbage. Stir, cover and cook for 7 minutes, stirring occasionally. Add a splash of water half way to help cabbage cook.
Add previously cooked chicken, give sauce a quick stir and add to the skillet. Gently stir to combine and cook for another 1-2 minutes or until sauce has thickened.
Turn off heat and garnish with green onion and sesame seeds. Serve immediately.
Notes
Store: Refrigerate covered for up to 5 days.
Reheat: By simmering stir fry on the stove with a splash of water or broth until heated through. Stir occasionally.