Prepare the flank steak by slicing it against the grain into thin, bite-sized strips.
In a small bowl, whisk together the coconut aminos, minced garlic, and grated fresh ginger to create the stir-fry sauce.
Heat the sesame oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips to the skillet in a single layer and season with sea salt and black pepper.
Sear the beef for 2 to 3 minutes until browned and caramelized, then remove the meat from the pan and set aside.
Add the broccoli florets to the same skillet with a tablespoon 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 sesame-ginger sauce over the mixture.
Toss all ingredients together for 1 minute until the sauce thickens slightly and coats the beef and broccoli evenly.
Garnish the dish with toasted sesame seeds and serve immediately.