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. Stir and cook for 1 minute until the chicken is lightly 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 evenly with the vegetables and chicken.
04 - Stir in the ketchup and soy sauce, mixing thoroughly until the rice turns a uniform reddish-orange 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 - Melt half of the butter in a non-stick skillet over medium-low heat. Pour in half of the egg mixture, 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 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. Place a paper towel over the top and gently press to refine the shape if needed.
09 - Repeat the omelette cooking, filling, and folding process with the remaining butter, egg mixture, and fried rice to make the second serving.
10 - Drizzle ketchup over the top of each omurice and sprinkle with chopped parsley if desired. Serve immediately while hot.