Slice the flank steak against the grain into very thin, bite-sized strips.
In a small bowl, whisk together the coconut aminos, grated fresh ginger, minced garlic, water, and toasted sesame oil to create the stir-fry sauce.
Heat the extra virgin olive oil in a large skillet or wok over medium-high heat until shimmering.
Add the beef strips to the pan in a single layer, season with sea salt and black pepper, and sear for 2 minutes per side until browned; remove the beef and set aside.
Add the broccoli florets to the same pan with an extra splash of water, cover with a lid, and steam for 3 minutes until they are tender-crisp and bright green.
Return the beef to the pan and pour the prepared sauce over the ingredients.
Toss everything together for 1 minute over high heat until the sauce thickens slightly and coats the beef and broccoli beautifully.
Transfer to a plate and garnish with sesame seeds before serving.