Soak the shiitake mushrooms in plenty of freshly boiled water for an hour.
Boil 2L of water in a large pot. Once the water comes to the boil, turn up the heat onto high and add the chicken frames. Allow to boil for 10 minutes and skim off any scum that rises to the surface.
Add all the chicken stock ingredients and the chicken breast to the pot. Once the water returns to the boil, continue to simmer on low - medium heat for 1 hr 15 mins. Every now and then remove the scum as it forms on the surface of the soup.
Check on the chicken breast after 15 minutes, If completely cooked through, then let it cool and then shred. Set aside until needed.
If you are using fresh quail eggs, boil them in a different pot on medium for 15 minutes. Set aside until needed.
After 1 hr 15 mins remove the chicken frames from the pot and strain the stock. Squeeze out as much liquid from the vegetables as you can.
Add the asparagus, peeled quail eggs, shredded chicken and shiitake mushrooms. NOTE: Before adding the sliced shiitake mushrooms, be sure to squeeze out as much liquid as possible.
Allow the soup to develop the flavours for another 20 minutes on low medium heat.
Swirl the soup with a large spoon in a circular motion and then add the beaten egg.
Combine the cornstarch with cold water and add to the pot. Stir until thickened.
Taste the soup and adjust if necessary. Serve and garnish while hot.
Cutting the vegetables into smaller pieces will help the soup absorb more of the flavours.