Slice the flank steak against the grain into very thin strips and season evenly with the sea salt and black pepper.
In a small glass bowl, whisk together the coconut aminos, minced garlic, grated fresh ginger, and red pepper flakes to create the stir-fry sauce.
Heat a large cast-iron skillet or wok over medium-high heat and add half of the sesame oil to coat the surface.
Place the beef strips in the hot skillet in a single layer and sear for 2 minutes until browned and caramelized, then transfer the beef to a clean plate.
Add the broccoli florets to the same skillet with a tablespoon of water, immediately covering with a lid to steam for 2-3 minutes until bright green and tender-crisp.
Remove the lid, return the beef to the pan, and pour the prepared sauce over the ingredients, tossing constantly for 1 minute until the sauce glazes the beef.
Remove from the heat, drizzle with the remaining sesame oil for a fragrant finish, and garnish with sesame seeds before serving hot.