Using a cast iron frying pan heat up the butter and miso until melted. Add some teryiaki sauce. When hot add mushrooms and fry them until golden brown. The miso will stick to the mushrooms and give them a meaty taste.
In a separate pot add water and bring to a boil. Once the mushrooms are brown dump the butter and mushrooms into the pot. Bring water to boil.
While water is coming to a boil, crack the eggs and place them in a bowl. Gently whisk them so that there are no bubbles.
When water is boiling slowly add the eggs to the water. Heat until they are cooked. Literally drop the eggs into the boiling soup. The slower you go the more wispy it comes out.