Prepare the flank steak by slicing it very thinly against the grain into bite-sized strips.
In a small bowl, whisk together the coconut aminos, minced garlic, and grated fresh ginger to create the stir-fry sauce.
Heat the avocado oil in a large skillet or wok over medium-high heat until shimmering.
Season the beef strips with sea salt and black pepper, then add them to the hot skillet in a single layer.
Sear the beef for 2 minutes without moving to develop a golden crust, then flip and cook for 1 additional minute before removing the beef from the pan and setting aside.
Add the broccoli florets to the same skillet with a splash of water; cover with a lid for 2 minutes to steam until vibrant green and tender-crisp.
Remove the lid and return the beef to the pan, pouring the prepared sauce over the mixture.
Toss everything together for 1 minute until the sauce thickens slightly and coats the beef and broccoli.
Turn off the heat and drizzle the toasted sesame oil over the dish, stirring gently to combine.
Plate the stir-fry immediately and garnish with sesame seeds for added crunch.