Rinse the dried shiitake mushrooms and place them in a bowl with water. Cover loosely with plastic wrap and microwave at 600W for 1 minute. Let sit for 10 minutes, then remove the mushrooms and reserve the soaking liquid.

Cut the chicken wings at the joints and place them in a pot. Add ginger, shiitake soaking liquid (add water if less than 300ml), sake, mirin, and the soaked shiitake mushrooms. Bring to a boil over medium heat and skim off any foam.