Cook the brown rice according to package instructions and set aside.
Whisk tamari, honey, grated ginger, and minced garlic in a small bowl to create the marinade.
Toss the sliced flank steak with sea salt, black pepper, and half of the marinade; let sit for 10 minutes.
Heat toasted sesame oil in a large skillet over medium-high heat.
Add the beef to the skillet in a single layer and sear until browned and caramelized, about 2-3 minutes per side.
Remove beef from the pan and add broccoli and carrots with a splash of water, covering to steam for 3 minutes.
Return beef to the pan, add the remaining marinade, and toss everything together until the sauce thickens and coats the beef.
Serve the beef and vegetables over the brown rice, garnished with sesame seeds and sliced green onions.