Slice the flank steak against the grain into very thin strips to ensure maximum tenderness.
In a small glass bowl, whisk together the tamari, toasted sesame oil, honey, minced garlic, and grated ginger.
Heat the avocado oil in a large stainless steel skillet or wok over medium-high heat until shimmering.
Add the beef strips in a single layer and sear without moving for 2 minutes, then toss and cook for 1 more minute until browned.
Remove the beef from the pan and add the broccoli florets with 2 tablespoons of water, covering with a lid to steam for 2 minutes.
Remove the lid, return the beef to the pan, and pour the sesame-tamari sauce over the mixture.
Toss everything together for 1 minute until the sauce thickens into a glossy glaze, then season with sea salt and black pepper.
Transfer to a plate and garnish with sesame seeds before serving.