Slice the flank steak against the grain into thin strips and season evenly with the sea salt and black pepper.
In a small glass bowl, whisk together the coconut aminos, minced ginger root, minced garlic, arrowroot powder, and water to create a slurry-based stir-fry sauce.
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 without moving for 2 minutes to develop a crust, then flip and cook for another minute before removing from the pan.
Add the broccoli florets to the hot pan with a splash of water, immediately covering with a lid for 2 minutes to steam until they are bright green and tender-crisp.
Remove the lid, return the beef to the pan, and pour the sauce mixture over the ingredients.
Toss everything constantly for 1 minute until the sauce thickens into a glossy glaze that coats the beef and broccoli perfectly.