Add all the "Sauce" ingredients to a medium bowl, whisk until fully combined.
If you have time, add the cubed chicken to a large ziplock bag and pour the sauce on top. Transfer to the fridge and marinate for at least 30 minutes or overnight, for extra flavor.
When ready to cook, place a stir fry wok or cast iron pan over medium-high heat.
Add 2 tablespoons of vegetable or canola oil, and once hot, add the broccoli florets. Toss and cook for 4-6 minutes, or until tender. Transfer cooked broccoli to a plate.
Add the chicken and the sauce to the skillet over high heat in one layer. If needed cook in batches.
Cook the chicken without moving for 1 minute, to get a nice sear on it. After that continue to cook while stirring and tossing, until the chicken is no longer pink and the sauce forms a glaze, about 7-8 minutes.
Return the cooked broccoli to the pan, and stir until the chicken and broccoli are heated through and everything is well coated in sauce, about 3 minutes.
Serve garnished with sesame seeds and chopped green onions.