Slice the flank steak against the grain into thin strips and season evenly with sea salt and black pepper.
In a small bowl, whisk together the coconut aminos, minced ginger, minced garlic, arrowroot powder, and water to create the stir-fry sauce.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat until shimmering.
Add the beef strips to the skillet in a single layer and sear until browned, about 2 to 3 minutes, then remove the beef and set it aside.
Add the broccoli florets to the same skillet with a splash of water, cover with a lid, and steam for 2 minutes 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 sauce thickens into a glossy glaze that coats the beef and broccoli.