For the wontons
Clean the shiitake mushrooms and remove the stems (save the stems for stock).
Dice the shiitake caps and place them in a medium bowl.
Cut the water chestnut and the asparagus into small pieces.
To a medium size cooking pan, add oil and heat for 1 minute. Add the ginger and sauté for 1 minute. Add the shiitake, water chestnut and asparagus and turn up the heat. Cook for 2 minutes.
Stir in soy sauce and sesame oil. Set aside the wonton filling and allow to cool.
Fill a small bowl with water. Arrange a wonton wrapper on a plate or work surface. Place about 1 teaspoon of the filling mix in the centre.
Dip your fingers in water and moisten the edges of the wonton wrapper.
Fold in half, over the filling, to create a triangle. Press the edges together to seal. Draw the side corners of the wrapper inward, join and press them together to seal, creating a loop.
Repeat until all the filling and wrappers are used.
To cook the wonton, bring a large pot of water to boil. Place the wontons in boiling water and cook for 4 minutes or until they float. Remove the wontons and place straight into serving bowls.
For the wonton soup
Place a large pot on a stove top with a medium heat. Heat the vegetable oil and sesame oil. Add the ginger and mushroom stems. Sauté for 1 minute, until fragrant.
Add the broth, raise the heat, add the cabbage, and bring it to a boil. Add the bok choy, if using, cook for 1 minute.
Remove the pot from the heat. Season with soy or salt to taste.
Ladle the broth into the wonton serving bowl and serve warm.