Place the flank steak in the freezer for 15 minutes to firm up, then slice it very thinly against the grain into bite-sized strips.
In a medium bowl, whisk together the coconut aminos, toasted sesame oil, honey, grated ginger, and minced garlic to create the marinade.
Add the beef to the bowl, tossing to coat thoroughly, and let it marinate for at least 10 minutes at room temperature.
While the beef marinates, steam the broccoli florets until they are bright green and crisp-tender, then set aside.
Heat a large cast-iron skillet over high heat and add the beef in a single layer, searing for 1-2 minutes per side until caramelized and cooked through.
Serve the beef over the cooked brown rice and steamed broccoli, garnishing with sliced green onions and sesame seeds.