Bring a large pot of water to boil and cook somen noodles according to package instructions (usually around 2 minutes).
Drain cooked somen and immediately dunk in ice water to cool.
Prepare your vegetables and kamaboko if you haven't already, slicing them thinly.
Make omelette: using one egg at a time, lightly beat the egg in a bowl, then pour into a heated and oiled skillet on stovetop. Cook over medium heat until the thin omelette is cooked through and remove to a cutting board. Repeat with the other egg.
When the omelettes have cooled down, slice into thin ribbons.
Assemble your somen salad by placing drained somen at the bottom of a large bowl. Arrange your sliced and shredded toppings on top of the noodles (in any pattern or formation you like).
Make salad dressing by mixing sugar, rice vinegar, oil, sesame oil, and soy sauce together until homogenous (I like to shake it in a mason jar).
Pour dressing over arranged salad and top with green onions. You can serve your salad like this, allowing guests to choose toppings as they like, or you can mix the salad together before serving. Somen salad is best eaten the day it is made.