Slice the flank steak against the grain into thin strips and season evenly with the sea salt and black pepper.
In a small bowl, whisk together the coconut aminos, sesame oil, minced ginger, and minced garlic to create the stir-fry sauce.
Heat the avocado oil in a large skillet or wok over medium-high heat until it is shimmering and very hot.
Add the beef strips in a single layer and sear for 2 minutes without moving them to develop a deep brown crust, then flip and cook for 1 additional minute.
Add the broccoli florets and 2 tablespoons of water to the skillet, then immediately cover with a lid to steam for 2 minutes until the broccoli is bright green and tender-crisp.
Remove the lid, pour the prepared sauce over the beef and vegetables, and toss constantly for 1 minute until the sauce thickens and coats everything in a glossy glaze.
Transfer the stir-fry to a plate alongside the warm brown rice and garnish with the sesame seeds for a final layer of texture.