A friend recently gave me Philip Pullman's 'Fairy Tales from the Brothers Grimm', I can't recommend it highly enough. This story is from there.

He says "As quite often in Grimm, we have two separate story types sewn together here. Once the hunter has the bird's heart and the wishing cloak, he could in theory go on to any kind of adventure. The story of the cabbage (sometimes translated as lettuce) which turns whoever eats it into a donkey has no logical connection with the first part of the story, but they fit together very well."