Soak kombu: Clean the kombu using a damp cloth to wipe the seaweeds without removing the white powdery coating. Place in a pot and cover with the water. Leave to soak for at least 30 minutes and up to half a day.
Heat kombu: Turn on the heat and almost bring it to a boil. Take it off the heat just before it starts to boil, and remove the kombu. Save it for the second dashi.
Bonito flakes: Let the liquid stand for about 5 minutes then add the dried bonito flakes. Bring to a boil again, skimming occasionally, and simmer for just 30 seconds when it comes to a boil. Turn off the heat and leave it for about 10 minutes until the bonito flakes sink to the bottom.
Strain: Line a sieve with a paper towel and strain the liquid. Squeeze the paper towel to release all the liquid. Keep the bonito flakes for the second dashi.
Store: The dashi will keep for 3 to 7 days in the fridge and about 3 weeks when frozen.
Second dashi, optional for later use:
Second dashi (optional): Place the cooked kombu and bonito flakes in a pot, cover with 1 liter/ 4 cups water, bring to a boil, and cook gently for 10 minutes. Leave it until the bonito flakes sink to the bottom of the pot and strain as shown before.
Soy sauce eggs:
Whisk the warm water, sugar, vinegar, and soy sauce in a bowl large enough to hold the 6 eggs.
Cook eggs: Bring a pot of water to a boil and cook the eggs for 6 minutes and 50 seconds. In the meantime, fill a bowl with ice cubes and cold water and place the eggs inside as soon as they are cooked. Leave for a few minutes, then peel.
Marinate: Place the eggs in the marinade and marinate for 2 to 6 hours. Remove and place in an airtight container; they will keep it in the fridge for 1 month. You can reuse the marinade to make a second batch of eggs (they were so good, I made a second batch immediately).
Heat the dashi gently and stir in the mirin, sake, soy sauce, and salt to taste.
Cook mushrooms: Clean and slice the mushrooms and cook them in 1 tablespoon oil until golden brown.
Cook the noodles according to the package's instructions. Soak the wakame in hot water according to the package's instructions. Chop the scallions and drain or defrost the corn kernels.
Serve: Place some of these ingredients in each bowl, pour the soup over and top with the halved eggs. Serve immediately.