Melt the butter in a Dutch oven over medium-low heat; add the shallots and cook until they are translucent.
Meanwhile, wash the cabbage and then slice it into four wedges. Remove the hard core pieces and shred or coarsely cut the wedges into strips.
Add the wine to the Dutch oven and continue cooking for 2 minutes.
Add the cabbage to the Dutch oven with the chicken stock and vinegar.
Bring the cabbage mixture to a simmer over medium heat. Cover the pan and reduce the heat to low; simmer for 15 minutes or until the cabbage is tender.
Arrange the cabbage in a serving bowl with the liquids from the pan.