Cook the noodles according to package instructions. Drain and rinse thoroughly under cold water to stop cooking and cool completely.
Prepare the toppings. Julienne the cucumber and carrot, slice the tomato, and cook the egg into a thin omelet. Slice into strips. Cut ham or chicken into matchsticks.
Make the dressing. In a small bowl, whisk together soy sauce, vinegar, water, sugar, sesame oil, and mustard until well combined.
Assemble each bowl. Divide noodles into four bowls. Neatly arrange toppings in colorful sections over the noodles.
Pour over the sauce or serve on the side for dipping. Garnish with pickled ginger, sesame seeds, and shredded nori if desired.
Chill and serve. Enjoy immediately or let the bowls chill in the fridge for 10 minutes before serving.