Slice the flank steak against the grain into very thin, bite-sized strips.
In a small glass bowl, whisk together the coconut aminos, toasted sesame oil, minced fresh ginger, and minced garlic to create the stir-fry sauce.
Heat the avocado oil in a large stainless steel skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips to the hot pan in a single layer, season with sea salt and black pepper, and sear undisturbed for 2 minutes to develop a deep brown crust.
Toss the beef, then add the broccoli florets and 1 tablespoon of water to the pan; cover immediately with a lid for 90 seconds to steam the broccoli until it is bright green and tender-crisp.
Remove the lid, pour the prepared sauce over the beef and broccoli, and stir-fry constantly for 1 minute until the sauce reduces into a glossy glaze.
Garnish with sesame seeds and serve immediately while steaming hot.