Slice the flank steak against the grain into very thin strips.
In a small bowl, toss the beef strips with arrowroot powder, sea salt, and black pepper until evenly coated.
Whisk together the tamari, water, minced ginger, and minced garlic in a separate small ramekin to create the stir-fry sauce.
Heat the avocado oil in a large skillet or wok over medium-high heat until shimmering.
Add the beef to the pan in a single layer and sear for 2 minutes until browned, then remove the beef and set aside.
Add the broccoli florets to the same pan with a splash of water, covering with a lid for 2 minutes to steam until bright green and tender-crisp.
Return the beef to the pan, pour in the tamari sauce mixture, and toss everything together for 1 minute until the sauce thickens and coats the ingredients.
Remove from heat and drizzle with the toasted sesame oil before serving.