Slice the flank steak against the grain into thin, bite-sized strips and season evenly with sea salt and black pepper.
In a small glass bowl, whisk together the coconut aminos, grated fresh ginger, minced garlic, and arrowroot powder until smooth.
Heat the toasted sesame oil in a large stainless steel skillet or wok over medium-high heat until shimmering.
Add the beef strips to the pan in a single layer and sear without moving for 90 seconds to develop a deep crust, then flip and cook for another minute before removing to a plate.
In the same skillet, add the broccoli florets and 2 tablespoons of water; cover immediately with a lid to steam for 2 minutes until bright green.
Remove the lid, return the beef and any accumulated juices to the pan, and pour the prepared sauce over the mixture.
Toss everything constantly for 1 minute until the sauce thickens into a glossy glaze that coats the beef and broccoli.
Transfer the stir-fry to a bowl over the warm brown rice and garnish with sesame seeds before serving.