In a small bowl, whisk together the coconut aminos, honey, toasted sesame oil, and arrowroot starch until smooth to create the stir-fry sauce.
Thinly slice the flank steak against the grain and season evenly with sea salt and black pepper.
Heat the avocado oil in a large skillet or wok over medium-high heat until shimmering.
Add the beef in a single layer and sear for 2 minutes until browned, then remove the beef from the pan and set it aside.
Add the broccoli florets to the same pan with a splash of water, cover, and steam for 3 minutes until bright green and tender-crisp.
Stir in the minced garlic and grated ginger, cooking 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 becomes glossy.
Serve the stir-fry immediately over the warm cooked brown rice.