01 - Crack the eggs into a mixing bowl. Add soy sauce, sesame oil, and white pepper. Beat vigorously with a whisk or fork until the mixture is uniform and slightly frothy.
02 - Heat 1 tablespoon of vegetable oil in a non-stick frying pan over medium-high heat. Add the julienned carrot, sliced bell pepper, spring onions, and bean sprouts. Stir-fry for 2 to 3 minutes until the vegetables are slightly tender but still crisp.
03 - Add the shredded cooked chicken to the pan, stir to combine with the vegetables, and cook for 1 additional minute. Remove the entire mixture from the pan and set aside.
04 - Add the remaining tablespoon of vegetable oil to the pan. Pour in the beaten egg mixture, tilting the pan to spread it into an even layer across the surface.
05 - As the eggs begin to set, gently lift the edges with a spatula, allowing the uncooked egg to flow underneath and cook evenly.
06 - When the omelette is mostly set but still slightly moist on top, spread the cooked vegetable and chicken mixture evenly over one half. Fold the other half over the filling and cook for 1 more minute.
07 - Slide the finished omelette onto a plate and serve immediately while hot.