01 - Heat vegetable oil in a large skillet over medium heat. Add diced chicken and cook until lightly browned and just cooked through, approximately 3-4 minutes.
02 - Add the chopped onion and diced carrot to the skillet. Sauté until vegetables are softened, about 2-3 minutes. Stir in frozen peas and cook for an additional minute.
03 - Add the cooked rice to the skillet, breaking up any clumps with a wooden spoon. Pour in ketchup and soy sauce, mixing thoroughly until the rice is evenly coated and heated through. Season with salt and black pepper to taste.
04 - Divide the fried rice into two equal portions. Shape each portion into an oval mound and place onto individual serving plates.
05 - In a mixing bowl, whisk together 4 large eggs, 2 tablespoons whole milk, and a pinch of salt until well combined.
06 - Heat 1/2 tablespoon butter in a nonstick skillet over medium heat. Pour in half the egg mixture, swirling to coat the pan evenly. As the eggs just begin to set but remain slightly runny on top, carefully slide one portion of fried rice onto one side of the omelet.
07 - Using a spatula, gently fold the other side of the omelet over the rice to form a half-moon shape. Carefully transfer to the serving plate, seam side down.
08 - Repeat the omelet cooking process with the remaining butter and egg mixture for the second portion of rice.
09 - Drizzle ketchup decoratively across the top of each omelet. Sprinkle with finely chopped fresh parsley if desired. Serve immediately while hot.