01 - Heat vegetable oil in a large skillet over medium heat. Add diced chicken and cook until lightly browned and cooked through. Add chopped onion and diced carrot, sautéing until softened, about 2-3 minutes. Stir in frozen peas.
02 - Add cooked rice to the skillet, breaking up any clumps with a wooden spoon. Pour in ketchup and soy sauce, mixing thoroughly until rice is evenly coated and heated through. Season with salt and black pepper to taste. Divide the fried rice into two equal portions and shape each into an oval mound. Place each mound on individual serving plates.
03 - In a mixing bowl, whisk together 4 large eggs, whole milk, and a pinch of salt until fully combined and slightly frothy.
04 - Heat half the butter in a nonstick skillet over medium heat. Pour in half the egg mixture, swirling the pan to create an even layer. Allow the eggs to set slightly while maintaining a creamy, runny consistency on top.
05 - Carefully slide one portion of fried rice onto one side of the partially set omelet. Using a spatula, gently fold the opposite side over the rice, creating a half-moon shape. Transfer to a serving plate with the seam side down. Repeat with remaining ingredients for the second portion.
06 - Drizzle ketchup in a decorative pattern across the top of each omelet. Sprinkle with freshly chopped parsley if desired. Serve immediately while hot.