Slice the flank steak against the grain into very thin strips and season with the sea salt and black pepper.
In a small glass jar, whisk together the coconut aminos, toasted sesame oil, minced fresh ginger, minced garlic, and arrowroot powder until smooth.
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 without moving for 1 minute, then toss and cook for 1 additional minute until browned.
Remove the beef from the skillet and set aside on a plate.
Add the broccoli florets to the hot skillet with a tablespoon of water, cover immediately, and steam for 2 minutes until bright green and tender-crisp.
Return the beef and any accumulated juices to the pan, then pour the sauce over the top.
Toss everything together for 1 minute until the sauce thickens into a glossy glaze that coats the beef and broccoli.
Transfer to a bowl and garnish with sesame seeds before serving hot.