Slice the flank steak against the grain into thin strips and season with sea salt and black pepper.
In a small bowl, whisk together coconut aminos, minced ginger, minced garlic, and arrowroot powder to create the stir-fry sauce.
Heat sesame oil in a large skillet or wok over medium-high heat until shimmering.
Add the beef strips in a single layer and sear until browned, about 2 minutes per side, then remove from the pan.
Add the broccoli florets to the same pan with a splash of water, covering for 2 minutes to steam until tender-crisp.
Return the beef to the pan and pour the sauce over the mixture, tossing constantly until the sauce thickens into a glossy glaze.
Serve the beef and broccoli over a bed of warm cauliflower rice.