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 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 to combine evenly with the vegetables and chicken.
04 - Add the ketchup and soy sauce, mixing thoroughly until the rice is evenly coated and turns a uniform reddish-orange color. Season with salt and black pepper to taste. Remove from heat and set aside to cool slightly.
05 - Crack the eggs into a mixing bowl. Add the milk and salt, then whisk until smooth and slightly frothy.
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, swirling the pan immediately to create a thin, even layer across the bottom.
07 - When the eggs are just set but still slightly runny on the surface, 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 a neat oval or 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 cooking, filling, and folding process using the remaining butter, egg mixture, and fried rice to create the second serving.
10 - Drizzle ketchup over the top of each omurice and sprinkle with chopped parsley if desired. Serve immediately while hot.