In a small bowl, whisk together all of the sauce ingredients and set aside.
Heat 1 tablespoon of sesame oil in a large wok or non-stick skillet over medium-high heat.
Season the chicken with salt and pepper then add the chicken to the wok. Cook and sauté for 6 minutes until golden brown and no longer pink. Remove the chicken from the wok and set aside.
Returning to the wok, add 1 tablespoon sesame oil, garlic, and ginger paste. Cook for 30 seconds.
Add the broccoli florets and cook for 4 minutes until tender and browned on the outside then remove and set aside.
Returning to the wok, add the sauce. Heat the sauce over medium-high heat for 1-2 minutes. The sauce will cook and start to thicken.
Add the cooked chicken and broccoli back to the wok with the sauce. Stir to evenly coat the ingredients with the sauce and heat through for 3 minutes.
Serve over rice and garnish with sesame seeds and red pepper flakes.