Slice the flank steak against the grain into thin, bite-sized strips.
In a small bowl, whisk together the coconut aminos, minced ginger, minced garlic, and arrowroot powder to create a slurry.
Steam the broccoli florets for 3 minutes until they are bright green and slightly tender, then set aside.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat.
Season the beef with sea salt and black pepper, then add it to the hot skillet in a single layer.
Sear the beef for 2 minutes per side until browned and caramelized, then toss in the steamed broccoli.
Pour the sauce mixture over the beef and broccoli, stirring constantly for 1 minute until the glaze thickens and coats everything.
Serve the stir-fry over the cooked brown rice and garnish with sesame seeds.