Thinly slice beef against the grain. The thinner the beef is sliced, the faster it will cook (it also marinates faster and makes a very flavorful dish). Using a sharp knife helps cut meat evenly.
Add sliced beef to a bowl, and mix it with the coconut aminos. Allow the beef to marinate while preparing the rest of the dish.
In a measuring cup or small bowl, whisk together all the stir fry sauce ingredients.
Add the broccoli to a large pan with a lid, along with about 1/4 cup of water. Heat the water to a simmer over high heat, and cover the pan for about 5 minutes, to allow the broccoli to steam. Remove the broccoli from the pan.
Into the same pan, drizzle the olive oil, and then add the marinated beef. Heat the pan to medium-high heat. Use a fork to spread the beef into an even layer so it cooks evenly. Cook each side for about 2-3 minutes, and then flip to cook the other side. Remove the beef from the pan.
Add the stir fry sauce to the pan. Heat it over medium-high heat, and bring the sauce to a simmer. Allow it to simmer for 2-3 minutes to thicken.
Add the steamed broccoli and cooked beef back into the pan, and toss to coat in the sauce.
Serve the beef and broccoli over rice, cauliflower rice, or other grain of choice. Garnish with sesame seeds and green onions if desired.