Slice the flank steak against the grain into thin, bite-sized strips and season with sea salt and black pepper.
In a small bowl, whisk together the coconut aminos, toasted sesame oil, minced garlic, and grated fresh ginger to create the glaze.
Heat the avocado oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips in a single layer and sear for 2 minutes until browned, then remove from the pan and set aside.
Add the broccoli florets to the same pan with a splash of water, cover immediately, and steam for 3 minutes until tender-crisp.
Return the beef to the pan, pour the sesame-ginger sauce over the mixture, and toss for 1 minute until the glaze thickens.
Serve the stir-fry over the warm cooked brown rice and garnish with a sprinkle of sesame seeds.