In a small bowl, whisk together the coconut aminos, minced fresh ginger, minced garlic, and arrowroot powder until the starch is fully dissolved.
Thinly slice the flank steak against the grain into bite-sized strips and season evenly with sea salt and black pepper.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips to the hot skillet in a single layer and sear for approximately 2 minutes until browned and caramelized, then remove the beef and set aside on a plate.
Add the broccoli florets to the same skillet with a tablespoon of water, cover with a lid, and steam-fry for 2-3 minutes until they are tender-crisp and bright green.
Return the seared beef and any accumulated juices to the skillet, then pour the prepared sauce over the mixture.
Toss everything constantly for 1 minute until the sauce thickens into a glossy glaze that coats the beef and broccoli.
Serve the stir-fry immediately over the warm brown rice and garnish with a sprinkle of sesame seeds.