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, toasted sesame oil, and arrowroot powder until no clumps remain.
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, searing for about 2 minutes without moving them to develop a deep brown crust, then flip and cook for 1 more minute before removing from the pan.
Add the broccoli florets to the hot pan with a tablespoon of water, immediately covering with a lid for 2 minutes to steam-fry until they are tender-crisp and vibrant green.
Remove the lid and stir in the minced garlic and grated fresh ginger, sautéing for 30 seconds until the aromatics are fragrant.
Return the seared beef and any accumulated juices to the pan, then pour the prepared sauce over the mixture.
Toss everything constantly for 1 minute as the sauce bubbles and thickens into a glossy glaze that coats the beef and broccoli.
Transfer to a plate and garnish with sesame seeds for a final crunch.