Toss the sliced beef with the soy sauce and cornstarch in a bowl and set aside while you prep the vegetables.
Microwave the noodle packs for 1 minute (or run them under hot water) so the block loosens. Pull the strands apart gently with your fingers.
Heat a large wok or skillet over high heat until very hot. Add 1 tbsp oil, then the beef in a single layer. Sear for 60 to 90 seconds, stirring once or twice, until just browned. Move the beef to a plate.
In the same pan, add the onion and carrot and stir-fry for 1 minute. Add the cabbage and stir-fry for 2 minutes, until the edges start to char but the cabbage is still crisp.
Add the noodles and 1 tbsp water. Toss for 1 to 2 minutes, lifting from the bottom, until the noodles are loose and hot.
Pour the yakisoba sauce around the edge of the pan and toss until every strand is coated and a little caramelized. Return the beef and add the green onions. Toss for 30 seconds.
Fry the eggs in a small pan with 1 tsp oil until the whites are set and the yolks are still runny.
Divide the noodles between two plates, top each with a fried egg, and add the ginger, bonito flakes and aonori if you have them. Serve right away.