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 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, tossing to combine all ingredients evenly.
04 - Pour in the ketchup and soy sauce, mixing thoroughly until the rice turns a uniform reddish-orange color. Season with salt and black pepper to taste. Remove from heat and let cool slightly.
05 - Whisk the eggs, milk, and salt in a mixing bowl until smooth and slightly frothy, about 30 seconds.
06 - Melt half the butter in a non-stick skillet over medium-low heat. Pour in half the egg mixture, tilting and swirling the pan to coat the bottom 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 a neat oval log.
08 - Slide the omurice onto a plate seam side down. Cover with a piece of 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 complete the second serving.
10 - Drizzle ketchup over the top of each omurice and sprinkle with chopped parsley if desired. Serve immediately while hot.