Slice the carrot lengthwise into thin strips.
Finely slice the shallot, garlic and ginger. Slice the shiitake, if needed.
Heat the oil in a wok. Stir-fry the shallot and carrot on a high heat for 2 minutes.
Add the garlic, ginger and stir-fry for another minute.
Add the shiitake, then stir-fry for another 3 minutes. Add soy sauce, rice vinegar and hoisin sauce, then the kale or cabbage. Turn down the heat and cook for a couple of minutes or until the cabbage has softened.
Stir in the sesame oil, then serve with sesame seeds scattered on top.