Slice the flank steak against the grain into thin, bite-sized strips.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat until shimmering.
Add the beef strips to the pan in a single layer and sear until browned, about 3 to 4 minutes, then remove and set aside.
In the same pan, add the minced garlic and grated fresh ginger, sautéing for 30 seconds until fragrant.
Add the broccoli florets and a splash of water, then cover the pan for 2 minutes to steam the broccoli until tender-crisp.
Remove the lid, return the beef to the pan, and pour in the coconut aminos.
Season with sea salt and black pepper, tossing everything together for 1 minute to glaze the ingredients.
Transfer to a plate and garnish with sesame seeds before serving.