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, water, and arrowroot powder until no clumps remain.
Heat the toasted sesame oil in a large stainless steel skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips in a single layer, searing for about 2 minutes until deeply browned, then remove the beef from the pan and set aside.
Add the broccoli florets to the same pan with a tiny splash of water, covering with a lid for 2 minutes to steam until they are vibrant green and tender-crisp.
Remove the lid and stir in the minced garlic and grated fresh ginger, sautéing for 30 seconds until the aromatics are fragrant.
Return the beef to the pan and pour the prepared sauce over the mixture, tossing constantly for 1 minute until the glaze thickens and coats every piece.
Transfer to a plate and garnish with sesame seeds before serving immediately.