Whisk the coconut aminos, honey, arrowroot, minced ginger, and minced garlic in a small bowl until the arrowroot is fully dissolved.
Slice the flank steak against the grain into thin strips and season evenly with the sea salt and black pepper.
Heat the sesame oil in a large wok or cast-iron skillet over medium-high heat until it begins to shimmer.
Add the steak strips in a single layer and sear without moving for 2 minutes to develop a crust, then flip and cook for 1 more minute.
Remove the steak from the pan and add the broccoli florets with a splash of water, covering immediately to steam for 2 minutes until crisp-tender.
Return the steak to the pan and pour the prepared sauce over the mixture, tossing constantly for 1 minute until the glaze is thick and glossy.
Transfer to a plate, garnish with the sesame seeds, and enjoy immediately.