Slice the flank steak against the grain into thin, bite-sized strips.
In a small glass jar, whisk together the coconut aminos, toasted sesame oil, minced ginger, minced garlic, and arrowroot powder.
Heat the avocado oil in a large cast-iron skillet or wok over medium-high heat until shimmering.
Add the beef to the hot skillet in a single layer, seasoning with sea salt and black pepper; sear until deeply browned, then remove from the pan.
Toss the broccoli florets into the same skillet with a tablespoon of water, covering briefly to steam until bright green and tender-crisp.
Return the beef to the skillet, pour the prepared sauce over the top, and stir-fry for 1 minute until the sauce becomes thick and glossy.