Thinly slice the flank steak against the grain into bite-sized strips.
In a small bowl, whisk together the coconut aminos, minced ginger, and minced garlic to create the stir-fry sauce.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat until shimmering.
Add the beef strips to the skillet in a single layer, seasoning with sea salt and black pepper; sear until browned, about 2-3 minutes.
Remove the beef from the pan and set aside, then add the broccoli florets and 1 tablespoon of water to the same skillet.
Cover the skillet with a lid for 2 minutes to steam the broccoli until it becomes a vibrant green and tender-crisp.
Return the beef to the skillet and pour the sauce over the mixture, tossing everything together for 1 minute until the sauce thickens slightly.
Serve the stir-fry immediately over the warm cooked brown rice and garnish with sesame seeds.