Slice the flank steak thinly against the grain and season with sea salt and black pepper.
In a small bowl, whisk together the coconut aminos, minced garlic, and grated fresh ginger to create the sauce.
Heat the avocado oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips in a single layer and sear for 2 to 3 minutes until browned, then remove the beef from the pan and set aside.
Add the broccoli florets to the same pan with two tablespoons of water and cover with a lid for 2 minutes to steam until tender-crisp.
Return the beef to the pan, pour the sauce over the mixture, and toss constantly for 1 minute until the sauce thickens and coats everything.
Remove from the heat, drizzle with toasted sesame oil, and garnish with sesame seeds before serving.