Heat the sesame oil and olive oil over medium-high heat in a large skillet.
Add the chicken and cook for approximately 5 minutes, until fully cooked. Remove from the pan to a plate and tent it with foil to keep it warm.
Add the broccoli to the skillet and cover, over medium heat, to steam until cooked to your liking.
While the broccoli is steaming, to a small bowl, mix together the chicken broth, soy sauce, brown sugar substitute, minced garlic and garlic paste until well combined. If you want a thicker sauce, add the xanthan gum or cornstarch now, too.
Add the chicken back to the skillet with the cooked broccoli.
Pour the sauce over the chicken and broccoli and stir to fully coat.
Turn heat to low and let simmer for a few minutes to let the flavors come together.
Sprinkle with sesame seeds before serving.
If you want to use frozen broccoli, steam it in the microwave then add it to the cooked chicken.If you're not watching carbs, you can use regular brown sugar.To thicken your sauce, add xanthan gum or cornstarch to the sauce before pouring over the chicken.