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, toasted sesame oil, minced garlic, and grated fresh ginger.
Heat the avocado oil in a large cast-iron skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips to the hot pan in a single layer, searing for 2 minutes per side until deeply browned and caramelized, then transfer to a clean plate.
Add the broccoli florets to the same skillet with two tablespoons of water, cover immediately, and steam for 3 minutes until bright green and tender-crisp.
Remove the lid and return the beef to the skillet, pouring the prepared sesame-ginger sauce over the top.
Toss everything together for 1 minute until the sauce thickens slightly and coats the beef and broccoli thoroughly.
Transfer to a plate and garnish with sesame seeds before serving immediately.