01 - Heat the 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 chicken is warmed through.
03 - Add the cold cooked rice to the pan, breaking apart 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 takes on a uniform reddish-orange color. Season with salt and black pepper to taste. Remove from heat and set aside to cool slightly.
05 - In a mixing bowl, whisk together the eggs, milk, and salt until smooth and slightly frothy.
06 - Melt half of the butter in a non-stick skillet over medium-low heat. Pour in half of the egg mixture, tilting and 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. Using a spatula, carefully fold both sides of the omelette over the rice, shaping it into an oval log.
08 - Slide the omurice onto a plate seam side down. Cover with a paper towel and gently press to refine the shape if needed.
09 - Repeat the omelette process with the remaining butter, egg mixture, and fried rice to create the second serving.
10 - Drizzle ketchup over each omurice and sprinkle with chopped parsley if desired. Serve immediately while warm.