01 - Heat vegetable oil in a large skillet over medium heat. Add the diced chicken and cook for 3 to 4 minutes, turning occasionally, until no longer pink throughout.
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 heated through.
03 - Add the cold cooked rice to the skillet, breaking apart any clumps. Stir-fry vigorously for 3 to 4 minutes until each grain is separated and evenly coated. Pour in the soy sauce and ketchup, season with salt and pepper, and toss until the rice is uniformly colored.
04 - Remove the skillet from heat. Divide the fried rice in half and shape each portion into a compact oval mound on a plate or cutting board. Set aside.
05 - In a mixing bowl, whisk together 2 large eggs, 1 tbsp of milk, and a pinch of salt until fully blended. Heat half of the butter in a nonstick skillet over medium-low heat until melted and lightly foaming.
06 - Pour the egg mixture into the skillet, tilting to form a thin even layer. Gently stir with chopsticks while tilting the pan until the eggs are just set but still slightly soft on top. Place one oval mound of fried rice along one edge. Use a spatula to fold the omelette over the rice, enveloping it completely. Carefully slide onto a serving plate, seam side down.
07 - Repeat the omelette process with the remaining 2 eggs, milk, salt, and butter to complete the second serving.
08 - Drizzle ketchup over each wrapped omelette in a zigzag or decorative pattern. Serve immediately while warm.