01 - Heat vegetable oil in a large skillet over medium heat. Add the chopped onion and diced carrot, cooking for 2–3 minutes until softened and fragrant.
02 - Add the diced chicken breast (or ham) 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 evenly with the vegetables and protein.
04 - Add the ketchup and soy sauce, stirring thoroughly until the rice is coated and turns a uniform reddish 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 the butter in a non-stick skillet over medium-low heat. Pour in half the egg mixture, 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 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.
08 - Slide the omurice onto a plate, seam side down. Cover with a piece of paper towel and gently press to shape if needed.
09 - Repeat the omelette cooking, filling, and folding process with the remaining butter, egg mixture, and fried rice to prepare the second serving.
10 - Drizzle ketchup over the top of each omurice and sprinkle with chopped parsley if desired. Serve immediately while warm.