Slice the flank steak against the grain into thin, bite-sized strips and season evenly with sea salt and black pepper.
In a small glass bowl, whisk together the coconut aminos, grated fresh ginger, and minced garlic to create the stir-fry glaze.
Heat a large skillet or wok over medium-high heat and add the sesame oil, swirling to coat the surface.
Add the beef strips to the hot skillet in a single layer and sear for 2-3 minutes until browned and caramelized, then remove the beef and set aside on a plate.
In the same skillet, add the broccoli florets and one tablespoon of water; immediately cover with a lid for 2 minutes to steam until tender-crisp.
Remove the lid, return the cooked beef to the pan, and pour the prepared ginger-sesame sauce over the mixture.
Toss all ingredients together for 1 minute over heat until the sauce thickens slightly and creates a glossy coating.
Transfer the stir-fry to a bowl over the warm brown rice and garnish with sesame seeds before serving.