Put the stock, ginger and garlic in a large pot and bring to a simmer. Cook for about 10 minutes.
Put 1 tablespoon of butter in a skillet and melt over a medium heat then add the mushrooms and cook for about 5 minutes until browned. Add the soy sauce, 2 tablespoons of miso and the rest of the butter. Cook for a little longer until the mushrooms are browned and the butter and miso is melted.
Bring a small saucepan of water to the boil and cook the eggs for 6-8 minutes until cooked to your liking. Remove from the water and submerge in cold water then peel.
Remove the ginger from the stock. Add the noodles and edmame and cook until the noodles are soft, about 4 minutes. Add the final tablespoon of miso to the stock and stir well.
Split the soup between 4 bowls. Halve the eggs and add to the soup then add the mushrooms. Sprinkle with the gochugaru and chilli flakes.
Nutrition information is an estimate and will vary depending on the ingredients used.