Thinly slice the flat iron steak against the grain. Thin slices help the beef cook quickly and stay tender.
Place the sliced beef in a small food-safe bag or container. Add the coconut aminos, grated fresh ginger, and chopped garlic. Seal and refrigerate for 1 hour.
When ready to cook, drain the beef and reserve the marinade. The reserved liquid will become the stir-fry sauce.
Bring a pot of water to a boil. Add the broccoli and blanch for 2 minutes. Drain thoroughly so excess water does not interfere with stir-frying.
Heat the coconut oil in a large wok or cast-iron skillet over medium-high heat.
Add the marinated beef and stir-fry for about 1–3 minutes, or until browned and cooked to your preferred doneness. Transfer the beef to a plate.
Add the broccoli to the hot skillet and stir-fry for about 3 minutes, until crisp-tender.
Pour the reserved marinade into the skillet and cook for about 2 minutes. For food safety, make sure the marinade reaches a thorough simmer while cooking.
Return the beef to the skillet and toss with the broccoli until everything is hot and evenly coated.
Add the fish sauce and toasted sesame oil. Toss briefly, then serve the keto beef and broccoli hot.