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, 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 frequently to ensure even heating and slight crisping.
04 - Pour in the ketchup and soy sauce, mixing thoroughly until the rice is evenly coated and turns a uniform reddish color. Season with salt and black pepper to taste. Remove from heat and let cool slightly.
05 - In a mixing bowl, whisk together the eggs, milk, and salt until the mixture is 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, immediately 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. Carefully fold both sides of the omelette over the rice using a spatula, shaping it into an oval or log form.
08 - Slide the omurice onto a serving plate with the seam side down. Cover with a piece of paper towel and gently press to refine the shape if needed.
09 - Repeat the omelette process using the remaining butter, egg mixture, and fried rice to create the second omurice.
10 - Drizzle ketchup over the top of each omurice and sprinkle with chopped parsley if desired. Serve immediately while hot.