01 - Heat vegetable oil in a large nonstick skillet over medium heat. Add the diced chicken and cook, stirring occasionally, until lightly golden and no longer pink throughout, about 4 to 5 minutes.
02 - Add the chopped onion and minced garlic to the skillet. Sauté until the onion turns translucent and fragrant, about 2 minutes. Stir in the frozen mixed vegetables and cook for an additional 2 minutes until tender.
03 - Add the cold cooked rice to the skillet, breaking up any clumps. Stir-fry vigorously until every grain is evenly coated and heated through. Pour in the soy sauce and ketchup, season with salt and pepper, and toss until the rice takes on a uniform reddish-amber color.
04 - Remove the skillet from heat. Divide the fried rice in half and shape each portion into a compact oval mound on a sheet of plastic wrap. Set aside and keep warm.
05 - In a mixing bowl, whisk together 2 large eggs, 1 tablespoon of milk, and a pinch of salt until fully blended and slightly frothy.
06 - Melt half the butter in a clean nonstick skillet over medium-low heat, tilting to coat the surface. Pour in the egg mixture and swirl gently to form a thin, even layer. As the edges begin to set, lightly stir the center with chopsticks or a silicone spatula, allowing soft curds to form while the top remains slightly wet and custard-like.
07 - Place one shaped rice mound along one side of the partially set omelette. Using a spatula, carefully fold the opposite edge of the omelette over the rice, enveloping it completely. Gently slide the wrapped omurice onto a serving plate, seam side down. Repeat the egg preparation and wrapping process for the second serving.
08 - Drizzle additional ketchup over each omurice in a zigzag or decorative pattern. Serve immediately while hot.