Slice the flank steak against the grain into very thin strips and season evenly with sea salt and black pepper.
In a small glass jar or bowl, whisk together the coconut aminos, minced ginger, minced garlic, and arrowroot powder until smooth.
Heat the avocado oil in a large stainless steel 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 per side until a golden crust forms, then transfer the beef to a plate.
Add the broccoli florets to the same pan with two tablespoons of water, immediately covering with a lid to steam for 3 minutes until vibrant green.
Remove the lid, return the beef to the pan, and pour the prepared sauce over the ingredients.
Toss everything together for 1 to 2 minutes until the sauce thickens into a glossy glaze that coats the beef and broccoli.
Turn off the heat, drizzle with toasted sesame oil, and garnish with sesame seeds before serving hot.