Slice the flank steak against the grain into very thin strips and season with sea salt and black pepper.
In a small glass bowl, whisk together the coconut aminos, fish sauce, and red pepper flakes to create the stir-fry sauce.
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 in a single layer and sear without moving for 90 seconds to develop a deep brown crust, then flip and cook for another 30 seconds before removing to a plate.
Add the broccoli florets to the hot pan with a tablespoon of water; cover immediately with a lid for 2 minutes to steam until bright green and tender-crisp.
Remove the lid and add the minced garlic and grated ginger, sautéing for 30 seconds until the aroma is released.
Return the beef and any accumulated juices to the pan, then pour the sauce over the mixture.
Toss everything together for 1 minute until the sauce thickens slightly and coats the beef and broccoli in a glossy finish.
Remove from heat, drizzle with toasted sesame oil, and garnish with sliced green onions and sesame seeds before serving.