01 - Heat vegetable oil in a large skillet over medium heat. Add the finely chopped onion and diced carrot, cooking for 2 to 3 minutes until softened and fragrant.
02 - Add the diced chicken breast and frozen peas to the skillet. Cook for approximately 1 minute, stirring occasionally, until the peas are thawed and the chicken is warmed through.
03 - Add the cold cooked rice to the pan, breaking up any clumps with a spatula. Stir-fry for 2 minutes, ensuring the rice is evenly coated with oil and heated through.
04 - Stir in the ketchup and soy sauce, mixing thoroughly until the rice turns a uniform reddish color. Season with salt and black pepper to taste. Remove from heat and let cool slightly while preparing the omelette.
05 - Whisk the eggs, milk, and salt together in a mixing bowl until smooth and slightly frothy.
06 - Melt half the butter in a non-stick skillet over medium-low heat. Pour in half of the egg mixture, swirling the pan to create a thin, even layer across the surface.
07 - When the eggs are just set but still slightly runny on top, mound half of the fried rice in the center. Carefully fold both sides of the omelette over the rice using a spatula, shaping it into an oval log.
08 - Slide the omurice onto a plate seam side down. Cover with a piece of paper towel and gently shape it if needed for a clean presentation.
09 - Repeat the omelette cooking, filling, and folding process with the remaining butter, egg mixture, and fried rice for the second serving.
10 - Drizzle ketchup over the top of each omurice and sprinkle with chopped parsley if desired. Serve immediately while warm.