Bring 3 quarts of water to a boil and add the soba noodles. Cook for 5 minutes and drain in a colander. Rinse the soba noodles with cold water until cool.
Put the eggs in a pot with enough water to cover them. Bring the water to a boil and turn off the heat. Let the eggs cook for 10 minutes with the lid on. Peel the eggs and cut in half.
Thinly slice lettuce, cabbage, carrot, and cucumber. Use cooking scissors to cut roasted seaweed into thin shreds.
Mix all the spicy red sauce ingredients in a bowl.
Assemble the noodle salad. To the soba noodles, add the vegetable toppings, eggs, and the spicy red sauce. Add a Sprinkle of Sesame seeds.
Notes
If you or someone else does not want the sauce to be spicy, omit the gochujang. It will still be delicious in a different way!