Whisk together ingredients for sauce including soy sauce, rice vinegar, sugar, sesame oil, ginger, and sesame seeds in a medium bowl. Set aside.
Bring a pot of water to a boil. Cook the noodles according to package directions. Drain and rinse in cold water.
Heat a non-stick pan over medium heat. Add 1 teaspoon oil. Whisk the egg and pour into the pan, spreading the egg in an even thin layer, similar to a crepe. Remove from heat and cut the egg into thin strips.
Bring a pot of water to a boil over high heat. Add the bean sprouts and blanch for 30 seconds. Remove from heat, drain and rinse in cold water.
Arrange the plates. Place the noodles in the center and arrange the chicken, ham, egg, cucumber, tomatoes, and bean sprouts around the ramen noodles. Top the noodles with the pickled red ginger. Pour dressing right before serving and mix with hot mustard if using.