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, toasted sesame oil, grated fresh ginger, minced garlic, and arrowroot powder to create the stir-fry sauce.
Heat the avocado 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 until deeply browned, then remove the beef from the pan and set aside on a plate.
Add the broccoli florets to the same pan with a splash of water, cover with a lid, and steam for 3 minutes until tender-crisp and bright green.
Return the beef and any accumulated juices to the pan, pour in the sauce mixture, and toss constantly for 1 minute until the sauce thickens into a glossy glaze.
Garnish with sesame seeds and serve immediately while hot.