Slice the flank steak against the grain into very thin strips to ensure tenderness.
Heat the avocado oil in a large skillet or wok over medium-high heat until shimmering.
Add the beef strips to the pan in a single layer, seasoning with sea salt and black pepper.
Sear the beef for 2-3 minutes without moving it to achieve a caramelized crust, then flip and cook for 1 more minute.
Remove the beef from the pan and set aside on a plate.
Add the broccoli florets to the same pan with a tablespoon of water, cover with a lid for 2 minutes to steam until bright green.
Remove the lid and add the minced garlic and grated ginger, sautéing for 30 seconds until fragrant.
Return the beef to the pan and pour in the coconut aminos and sesame oil, tossing everything to coat.
Cook for 1 minute until the sauce has slightly thickened and everything is well combined.
Serve the stir-fry immediately over the warm brown rice and garnish with sesame seeds.