Slice the flank steak against the grain into very thin strips and season them with the sea salt and black pepper.
In a small ramekin, whisk together the tamari, toasted sesame oil, and arrowroot powder until the powder is fully dissolved.
Heat the avocado oil in a large stainless steel skillet or wok over high heat until it begins to shimmer.
Add the beef strips in a single layer, searing without moving for 90 seconds to develop a deep brown crust, then flip and cook for another minute before removing from the pan.
Add the broccoli florets to the hot pan with two tablespoons of water, then cover immediately with a lid to steam for 2 minutes until bright green and tender-crisp.
Remove the lid and add the minced garlic and grated ginger, sautéing for 30 seconds until the aromatics are fragrant.
Return the beef to the pan, pour the tamari mixture over the top, and toss everything together for 1 minute until the sauce thickens into a glossy glaze.