Place 4 eggs in a bowl, add in the water, pinch of salt and pepper to taste. Beat with a fork and set aside
Slice the leeks thinly in a diagonal manner and place them in large pot of water and wash them and let them sit for about 5 minutes. Use your hands to remove the leeks to a large plate (the sand and dirt sink to the bottom)and discard the sandy water. Repeat this for two more times or until the water is no longer sandy.
Set aside and peel the carrot and shred it.
Preheat a large non-stick pan. When it's hot, add in 2 Tbsp of the cooking oil. Add the leeks and carrot to the pan and saute until they are soft, about 10 minutes or so. Remove from the wok and let it cool down. Add this cool down leek mixture into the beaten eggs and mix everything
Preheat a large non-stick pan again add in 1 Tbsp of the cooking oil. Pour in half of the egg mixture onto the middle of the pan and swirl the pan to cover the surface evenly. Let it cook until the bottom is no longer runny, gently flip it over to the other side. if they break apart, that's okay, it doesn't have to be in large circle. Let the other side cook to golden brown. Remove and place on a plate. Place another 1 Tbsp of oil into the pan again and repeat with the rest of the egg mixture. Serve immediately as part of multi-course meal