Slice the flank steak against the grain into thin, bite-sized strips.
In a small bowl, whisk together the coconut aminos, minced fresh ginger, and red pepper flakes.
Heat the avocado oil in a large skillet or wok over medium-high heat until it begins to shimmer.
Add the beef strips in a single layer and sear until browned, about 2 minutes per side, then remove the beef from the pan and set aside.
Add the broccoli florets to the same pan with a splash of water, covering for 2 minutes to steam until bright green and crisp-tender.
Stir in the minced garlic and cook for 30 seconds until fragrant.
Return the beef to the pan and pour in the coconut aminos mixture and the toasted sesame oil.
Toss everything together for 1-2 minutes until the sauce coats the ingredients and the beef is cooked through.
Garnish with sesame seeds and serve immediately.