Slice the flank steak against the grain into thin, bite-sized strips and season with sea salt and black pepper.
Mince the garlic and grate the fresh ginger, then thinly slice the green onion, keeping the white and green parts separate.
Heat a large skillet or wok over medium-high heat and add the toasted sesame oil.
Add the beef strips to the hot skillet in a single layer and sear until browned, about 2-3 minutes, then remove and set aside.
In the same skillet, add the broccoli florets and a splash of water, covering for 2 minutes to steam until tender-crisp.
Stir in the garlic, ginger, and the white parts of the green onion, sautéing for 1 minute until fragrant.
Return the beef to the skillet and pour in the coconut aminos, tossing everything together for 1-2 minutes until the sauce coats the ingredients.
Serve the stir-fry over the warm cooked brown rice and garnish with sesame seeds and the remaining green onion tops.