Slice the flank steak against the grain into thin strips and season evenly with sea salt and black pepper.
In a small glass bowl, whisk together the coconut aminos, minced ginger, minced garlic, arrowroot powder, and water to create the stir-fry sauce.
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 for 2-3 minutes until browned and caramelized, then remove the beef from the pan and set aside.
Add the broccoli florets to the same pan with a splash of water, covering with a lid for 2 minutes to steam until they are tender-crisp and bright green.
Return the beef to the pan and pour the prepared sauce over the mixture.
Toss everything together for 1-2 minutes until the sauce thickens into a glossy glaze that coats the beef and broccoli.
Remove from heat and drizzle with toasted sesame oil before serving immediately.