Slice the flank steak against the grain into very thin strips and season evenly with sea salt and black pepper.
Heat the avocado oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips to the hot pan in a single layer and sear for 2 minutes until deeply browned, then remove the beef and set it aside on a plate.
In the same pan, add the broccoli florets and two tablespoons of water, then cover with a lid for 2 minutes to steam the broccoli until tender-crisp.
Remove the lid and push the broccoli to the sides of the pan, adding the minced garlic and grated ginger to the center to sauté for 1 minute until fragrant.
Return the seared beef and any collected juices to the pan, then pour in the coconut aminos and toasted sesame oil.
Toss all ingredients together for 1 minute over high heat to allow the sauce to thicken slightly and coat the beef and broccoli.
Remove from heat and garnish with sesame seeds before serving immediately.