Slice the flank steak against the grain into thin strips and season evenly with sea salt and black pepper.
In a small glass bowl, whisk together the coconut aminos, toasted sesame oil, 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 until deeply browned, then remove the beef and set aside on a plate.
Add the broccoli florets to the same pan with two tablespoons of water; cover immediately and steam for 2 minutes until bright green and tender-crisp.
Return the beef and any accumulated juices to the pan, then pour the prepared sauce over the mixture.
Toss everything together constantly for 1 minute until the sauce thickens into a glossy glaze that coats the beef and broccoli.
Transfer to a plate and garnish with sesame seeds before serving immediately.