Slice the flank steak against the grain into thin, bite-sized strips.
Mince the garlic and grate the fresh ginger using a microplane.
Heat the olive oil in a large skillet or wok over medium-high heat until shimmering.
Add the beef strips to the pan, seasoning with the sea salt and black pepper, and sear until browned on all sides.
Remove the beef from the pan and set it aside on a plate.
Add the broccoli florets to the same pan with a splash of water, covering for 2 minutes to steam-soften.
Return the beef to the pan along with the garlic, ginger, coconut aminos, and toasted sesame oil.
Toss everything together for 1-2 minutes until the sauce coats the ingredients and the broccoli is tender-crisp.
Garnish the stir-fry with sesame seeds before serving immediately.