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 frothy.
02 - Heat 1 tablespoon of vegetable oil in a non-stick frying pan over medium-high heat until the oil shimmers.
03 - Add the julienned carrot, sliced bell pepper, spring onions, and bean sprouts to the pan. Stir-fry for 2 to 3 minutes until the vegetables are slightly tender but still crisp.
04 - Add the shredded cooked chicken to the vegetables, stir to combine, and cook for 1 additional minute. Remove the entire mixture from the pan and set aside.
05 - 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.
06 - As the eggs begin to set, gently lift the edges with a spatula, allowing the uncooked egg to flow underneath and cook evenly.
07 - When the omelette is mostly set but still slightly moist on top, spread the cooked vegetable and chicken mixture evenly over one half of the omelette.
08 - Fold the other half of the omelette over the filling. Cook for 1 more minute, then slide onto a plate and serve immediately.