For the pak choi with shiitake, cut the stem of the pak choi into small pieces and separate the leaves from each other. Wash, drain and cut into strips. Twist off the stems of the mushrooms, cut the heads into strips.
Stir-fry shiitake mushrooms in a wok in the two types of oil until they stop releasing juice. Add garlic and ginger and continue to stir-fry for 1 minute. Add pak choi and stir-fry until tender.
Stir soy sauce through with vinegar and cornstarch. Add to the frying pan and bring to a boil once until everything is nice and glossy together.
Arrange the pak choi with shiitake and serve.