For the marinated beef, place the beef into a bowl along with the soy sauce, sesame oil and lime zest and juice and season with salt and freshly ground black pepper. Leave to marinate for at least five minutes, ideally 30 minutes.
Heat the olive oil in a frying pan over a high heat, place the marinated beef into the pan and stir fry for 2-3 minutes, or until cooked to your liking. Remove from the heat and set aside in a warm place.
For the egg-fried rice, heat the vegetable oil in a wok, add the beaten eggs and stir well to cook the eggs quickly.
Add the cooked rice, peas and sesame oil to the wok, stir well and cook for 2-3 minutes.
To serve, transfer the rice to a bowl, top with the beef and drizzle over the soy sauce.