Slice the flank steak against the grain into thin, bite-sized strips to ensure maximum tenderness.
In a small bowl, whisk together the coconut aminos, minced ginger, minced garlic, and arrowroot powder until the mixture is smooth.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips to the pan and season with sea salt and black pepper, searing for 2-3 minutes until browned but not fully cooked through.
Remove the beef from the pan and set aside, then add the broccoli florets and sliced carrots to the pan with a splash of water.
Cover the pan and steam the vegetables for 3 minutes until they are tender-crisp and bright green.
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 everything.
Serve the stir-fry immediately over the warm brown rice and garnish with toasted sesame seeds.