Place the flank steak in the freezer for 15 minutes to firm up, then slice it against the grain into very thin strips.
In a medium glass bowl, whisk together the tamari, toasted sesame oil, honey, grated fresh ginger, minced garlic, sea salt, and black pepper.
Add the steak strips to the marinade, tossing well to coat every piece, and let it sit for at least 20 minutes at room temperature.
While the beef marinates, steam the broccoli florets and shredded carrots until they are vibrant and crisp-tender.
Heat a large cast-iron skillet over medium-high heat until it is smoking slightly.
Add the beef to the hot skillet in a single layer, working in batches if necessary, and sear for 1-2 minutes per side until deeply browned and caramelized.
Serve the beef over the warm brown rice and steamed vegetables, garnishing with sesame seeds and sliced green onions.