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 until the chicken is warmed through and the peas are bright green.
03 - Add the cold cooked rice to the pan, breaking up any clumps with a spatula. Stir-fry for 2 minutes, tossing frequently to ensure even heating and slight toasting.
04 - Pour in the ketchup and soy sauce, mixing thoroughly until every grain of rice is coated and turns a uniform reddish-orange color. Season with salt and black pepper to taste. Remove the pan from heat and let the rice cool slightly.
05 - In a mixing bowl, whisk together the eggs, milk, and salt until the mixture is smooth and slightly frothy, about 30 seconds of vigorous whisking.
06 - Melt half of the butter in a non-stick skillet over medium-low heat, tilting to coat the surface. Pour in half of the egg mixture and immediately swirl the pan to create a thin, even layer across the bottom.
07 - When the eggs are just set on the bottom but still slightly runny on top, mound half of the fried rice in the center of the omelette. Carefully fold both sides over the rice using a spatula, gently shaping it into an oval log.
08 - Slide the omurice onto a plate seam side down. Place a paper towel over the top and gently press to refine the oval 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 hot.