Slice the flank steak against the grain into very thin strips and season evenly with sea salt and black pepper.
In a small mixing bowl, whisk together the tamari, honey, and sesame oil until the honey is fully dissolved.
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, searing for about 2 minutes until browned and caramelized, then remove the beef and set it aside on a plate.
Add the broccoli florets to the same pan with a splash of water, immediately covering with a lid for 2 minutes to steam the broccoli until it is bright green and tender-crisp.
Remove the lid and stir in the minced garlic and grated fresh ginger, sautéing for 30 seconds until highly fragrant.
Return the cooked beef and any accumulated juices to the pan, then pour the tamari-sesame glaze over the top.
Toss everything together for 1 minute until the sauce thickens and coats the beef and broccoli, then serve immediately garnished with sesame seeds.