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 retain their crunch.
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 on a plate.
04 - Add the remaining tablespoon of vegetable oil to the pan. Pour in the beaten egg mixture, tilting the pan gently to spread it into an even, thin layer across the surface.
05 - As the eggs begin to set around the edges, gently lift each edge with a spatula, allowing the uncooked egg on top to flow underneath and cook evenly.
06 - When the omelette is mostly set but still slightly moist on the surface, spread the reserved vegetable and chicken mixture evenly over one half. Carefully fold the opposite half over the filling using the spatula.
07 - Cook the folded omelette for 1 more minute to seal and warm through. Slide it gently onto a plate and serve immediately while hot.