1. Cut the ginger into fine matchsticks. Put dried shiitake in saucepan with tight-fitting lid. Add ginger, pour in cold dashi, and bring to a boil. Clamp on the lid, lower heat, and let simmer for 15 minutes.
2. Meanwhile, put the saucepan of water for noodles. Toward the end of the broth’s 15 minutes simmering time, cook the noodles following package instructions, then drain and refresh under cold running tap.
3. Fill saucepan again with water. Bring to a boil, add the egg, and simmer for 6 1/2 mins.
4. While the broth is simmering, trim ends of baby bok choy and tear off the leaves. Separate the stems in one pile and leaves in another.
5. Quarter the radishes lengthways. When broth had its 15 minutes, bring to a rolling boil, and then add the bok choy stems and radishes. Bring it back to a boil then add leaves and turn off heat. Put a lid on.
6. When the eggs are ready, pour out the boiling water, and then run cold water into the pan until the egg cools enough to peel.
7. Put the drained noodles, broth and vegetables, cut egg in half lengthways and add all to the soup. Sprinkle scallions and red pepper over the top.