01 - Heat vegetable oil in a large nonstick skillet over medium heat. Add the diced chicken and cook for 3 to 4 minutes, stirring occasionally, until lightly browned and cooked through with no pink remaining.
02 - Add the chopped onion and minced garlic to the skillet. Sauté for 2 to 3 minutes until the onion turns translucent and fragrant. Stir in the frozen mixed vegetables and cook for an additional 2 minutes until warmed through.
03 - Add the cold cooked rice to the skillet, breaking apart any clumps. Stir-fry for 3 to 4 minutes until each grain is evenly coated and heated through. Pour in the soy sauce and ketchup, then season with salt and pepper. Continue stirring until the rice is uniformly colored and well seasoned.
04 - Remove the skillet from heat. Divide the fried rice into two equal portions and shape each into a compact oval mound on a plate or cutting board. Set aside while preparing the omelette.
05 - Crack the eggs into a mixing bowl, add the milk and salt, then whisk until fully blended and slightly frothy. Divide the mixture equally into two portions.
06 - Melt half the butter in a clean nonstick skillet over medium-low heat, tilting to coat the surface evenly. Pour in one portion of the egg mixture while simultaneously swirling the pan to create a thin, even layer across the bottom.
07 - Gently stir the eggs with chopsticks or a spatula in small circular motions for 30 to 60 seconds. Stop when the bottom is set but the surface remains slightly soft and custardy.
08 - Carefully slide one oval rice mound onto one half of the partially set omelette. Using a spatula, lift the opposite edge of the omelette and fold it over the rice, enveloping it completely. Gently roll or slide the wrapped omurice onto a serving plate with the seam facing down.
09 - Wipe the skillet clean if needed, then repeat the omelette cooking and wrapping process with the remaining butter, egg mixture, and second rice mound.
10 - Drizzle ketchup over each omurice in a zigzag or decorative pattern. Serve immediately while hot.