In a large saucepan, combine the konbu and water and heat over medium-low heat almost to the boiling point. Remove the konbu just before the mixture comes to a boil and discard. Add the bonito flakes and allow to steep for 10 seconds, or just until the mixture comes to a boil.
Turn off the heat and skim any foam that has come to the surface of the liquid. Allow the mixture to stand for 2 minutes, then strain through a fine mesh sieve or cheesecloth. Discard bonito flakes and return the dashi to the saucepan over low heat.
For the soup:
Add the mushrooms to the dashi and allow to steep over low heat until the mushrooms are softened, about 10 minutes. Stir in the soy sauce, white and brown miso and scallions and combine well. Season the shrimp with the salt and white pepper, add to the soup and continue to cook until just cooked through, 2 to 3 minutes. Divide the noodles evenly among the bowls; pour the miso and shrimp over the noodles. Serve immediately.