Slice the flank steak against the grain into thin, bite-sized strips.
Season the beef strips evenly with the sea salt and black pepper.
Heat the extra virgin olive oil in a large skillet or wok over medium-high heat.
Add the beef to the hot pan in a single layer and sear for 2 minutes until browned, then remove and set aside.
Lower the heat to medium and add the toasted sesame oil, garlic, and ginger to the same pan.
Sauté the aromatics for 30 seconds until fragrant, being careful not to burn the garlic.
Add the broccoli florets and water to the pan, then cover with a lid to steam for 2-3 minutes until tender-crisp.
Remove the lid and return the seared beef to the pan along with the coconut aminos.
Toss everything together for 1 minute until the sauce coats the beef and broccoli.
Serve the stir-fry over the cooked brown rice and garnish with sesame seeds.