01 - Heat vegetable oil in a skillet over medium heat. Add the onion and carrot, cooking for 2–3 minutes until softened.
02 - Add the diced chicken and frozen peas to the skillet. Cook for 1 minute, stirring occasionally.
03 - Add the cold rice to the pan, breaking up any clumps. Stir-fry for 2 minutes until the grains are separated and lightly toasted.
04 - Stir in the ketchup and soy sauce, mixing thoroughly until the rice is evenly coated and turns a uniform reddish color. Season with salt and pepper to taste. Remove from heat and let cool slightly.
05 - In a mixing bowl, whisk together the eggs, milk, and salt until smooth and slightly frothy.
06 - Heat half the butter in a non-stick skillet over medium-low heat. Pour in half the egg mixture, swirling the pan to coat it in a thin, even layer.
07 - When the eggs are just set but still slightly runny on top, mound half 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 paper towel and gently shape if needed.
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 each omurice and sprinkle with chopped parsley, if desired. Serve immediately.