Slice the flank steak against the grain into very thin strips to ensure maximum tenderness.
In a small glass bowl, whisk together the tamari, minced fresh ginger, minced garlic, sea salt, and black pepper to create the stir-fry sauce.
Heat the toasted sesame oil in a large stainless steel skillet or wok over medium-high heat until the oil is shimmering.
Add the beef strips in a single layer and sear without moving for 2 minutes to develop a crust, then toss and cook for 1 additional minute.
Remove the beef from the pan and set aside; immediately add the broccoli florets and two tablespoons of water to the hot pan.
Cover the pan with a lid for 3 minutes to steam the broccoli until it is bright green and fork-tender.
Return the beef to the skillet, pour the tamari sauce mixture over the ingredients, and stir-fry for 1 minute until the sauce is glossy and coats everything.
Transfer the stir-fry to a plate and garnish with the sesame seeds for a final crunch before serving.