Put the dried shiitake mushrooms in a saucepan that has a tight fitting lid. Add the ginger and pour in the dashi, bring to a boil and clamp on the lid. Reduce the heat and let it simmer for 15 minutes.
Meanwhile chop the bok choy separating the white and green parts. Cook the ramen noodles with the seasoning packet in 1 cup boiling water. Mix the miso with the soy sauce and sesame oil. Add to the dashi water.
Add the white parts of bok choy to the dashi water. Pour in the ramen noodles with the water. Cook 2 minutes. Add the green parts of the bok choy and green onions. Serve with a soft boiled egg if desired.