Slice the flank steak against the grain into thin, bite-sized strips to ensure maximum tenderness.
In a small bowl, whisk together the coconut aminos, minced ginger, minced garlic, and arrowroot powder until the mixture is smooth.
Heat the avocado oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips in a single layer, seasoning with sea salt and black pepper, and sear for 2 minutes until well-browned.
Toss in the broccoli florets and 2 tablespoons of water, then immediately cover with a lid for 2 minutes to steam the broccoli to a vibrant green.
Remove the lid, pour in the sauce mixture, and stir constantly for 1 minute until the sauce thickens into a glossy glaze.
Remove from the heat and drizzle with toasted sesame oil and a sprinkle of sesame seeds before serving.