Slice the flank steak against the grain into thin, bite-sized strips and season evenly with sea salt and black pepper.
In a small glass bowl, whisk together the coconut aminos, minced ginger, minced garlic, water, and arrowroot powder to create a smooth sauce slurry.
Heat the toasted sesame oil in a large stainless steel skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips in a single layer and sear for 2 minutes without moving them to develop a deep brown crust, then flip and cook for 1 more minute before removing from the pan.
Add the broccoli florets to the same pan with a tiny splash of water, covering with a lid for 2 minutes to steam-fry until they are tender-crisp and vibrant green.
Return the beef to the pan, pour the prepared sauce over the mixture, and toss constantly for 60 seconds until the sauce thickens into a beautiful, glossy glaze.