Slice the flank steak against the grain into thin strips and season evenly with the 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 sauce.
Heat the avocado oil in a large stainless steel skillet or wok over high heat until it begins to shimmer.
Add the beef strips in a single layer and sear for 2 minutes until deeply browned, then transfer the beef to a clean plate.
Add the broccoli florets and water to the same skillet, immediately covering with a lid for 2 minutes to steam until vibrant green and crisp-tender.
Remove the lid, return the seared beef to the skillet, and pour in the prepared ginger-garlic sauce.
Toss everything together for 1 minute over high heat until the sauce thickens slightly and coats the beef and broccoli.
Remove from heat, drizzle with the toasted sesame oil, and sprinkle with sesame seeds before serving hot.