In a bowl, mix beaten eggs, milk, and a pinch of salt and pepper.

Place the frozen yakisoba in a microwave-safe container and heat it in a 600W microwave according to the package instructions.

Heat vegetable oil in a frying pan over medium heat, pour in the egg mixture, and stir gently with chopsticks until it reaches a soft, half-cooked consistency. Place it over the heated yakisoba.

For the cheese sauce, tear the cheese slices into a microwave-safe container, add milk and a pinch of salt and pepper, cover loosely with plastic wrap, and microwave at 600W for 30 seconds. Stir until smooth, then pour over the eggs and yakisoba.