Make the sauce: whisk together the soy sauce, chicken broth, honey, corn starch, sesame seed oil, grated ginger, minced garlic, red pepper flakes, and pepper until the honey and cornstarch are completely dissolved.
Heat one teaspoon of sesame seed oil and half a tablespoon of light olive oil in a wok or heavy bottom skillet and brown the chicken pieces over medium-high heat until fully cooked. Season with salt and pepper and set aside.
Add one tablespoon of olive oil to the skillet and stir fry the sliced onions, mushrooms, and broccoli florets for about three minutes over medium-high heat.
Stir the sauce and pour it into the skillet. Cook for 3-4 minutes until thick.
Return the chicken to the skillet and cook until heated through. Serve with sesame seeds on top and over freshly cooked white rice.