Heat a large non-stick pan or wok over hight heat with some vegetable oil.
Add the beef and spread it around the pan evenly.
Do not stir or turn the beef for a few minutes. This will allow the beef to develop a sear with a nice, caramelised crust.
Once the beef has developed a nice sear, use a spoon to turn the meat over.
Immediately season the meat generously with sea salt and freshly cracked white pepper.
You do not need to cook the meat completely.
Remove the beef with a slotted spoon to a large plate.
Add a bit more oil to the pan.
Sauté the onions and garlic for 1 to 2 minutes, or until the onions have softened slightly.
Add the broccoli florets and stir everything together.
Cover the pan with a lid for 1 to 3 minutes, or until the broccoli is cooked but still crisp.
Push the vegetables to one side of the pan. Or, if your pan is quite small, simply remove the vegetables to a large plate.
If necessary, add a touch of oil to the pan.
Break both eggs into the pan.
Immediately, start scrambling the eggs with a wooden spoon.
Cook the scrambled eggs until they have just set.
Try to break up the scrambled eggs into large chunks.
Add the noodles to the pan, together with the vegetables and most of the sauce. Reserve 1-2 tablespoons of the sauce for later.
Stir everything together to distribute the sauce evenly.
Continue to cook over high heat for a few minutes until all of the ingredients are piping hot.
Taste for seasoning. If the stir-fry needs more flavour, add some or all of the remaining sauce.
Stir the cooked meat through the mixture, together with any meat juices on the plate.
Garnish with coriander (cilantro) and red chillies or
Pickled Chillies (if using).
Squeeze lime juice over the noodles immediately before serving.