Slice the flank steak against the grain into thin strips and season with the sea salt and black pepper.
In a small bowl, whisk together the coconut aminos, toasted sesame oil, grated fresh ginger, minced garlic, and arrowroot powder until smooth.
Heat the avocado oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips in a single layer and sear without moving for 2 minutes to develop a crust, then flip and cook for 1 more minute before removing from the pan.
Add the broccoli florets to the same pan with two tablespoons of water, then cover with a lid for 2 minutes to steam until tender-crisp.
Return the beef to the skillet and pour the prepared sauce over the mixture.
Toss everything constantly for 1 minute until the glaze thickens and coats the beef and broccoli evenly.
Transfer to a plate and garnish with sesame seeds before serving.