Slice the flank steak against the grain into very thin strips and toss in a bowl with arrowroot powder, sea salt, and black pepper until lightly coated.
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, working in batches if necessary to avoid crowding, and sear undisturbed for 2 minutes to develop a crispy brown crust.
Flip the beef and cook for an additional 60 seconds, then remove from the pan and set aside on a plate.
Add the broccoli florets to the same pan with a tablespoon of water, immediately covering with a lid for 2 minutes to steam them until tender-crisp.
Remove the lid and add the minced garlic and grated fresh ginger, stirring constantly for 30 seconds until highly fragrant.
Return the crispy beef to the pan and pour in the coconut aminos and toasted sesame oil.
Toss all ingredients together for 1 minute over high heat until the sauce thickens slightly and glazes the beef and broccoli.
Garnish with thinly sliced green onions and serve immediately while the beef is at its crispiest.