Separate the leaves of cabbage. Cut away and discard the tough ribs, then cut the cabbage leaves into thin strips.
Heat the oil in a medium saucepan over medium heat until the oil slides easily across the pan. Add a little of the cabbage and salt and pepper. Cook, stirring, until the cabbage wilts, then add a little more. Continue cooking, adding seasoning and stirring until all the cabbage is wilted.
Add the caraway seed and cook, stirring, for about 1 minute. Add the wine and vinegar and bring to a simmer. Sprinkle the sugar over the cabbage and mix well.
Reduce the heat to medium-low, partially cover and gently simmer, stirring occasionally, until most of the liquid has evaporated and the cabbage is soft and shiny, about 45 minutes. Remove the cabbage from the heat and allow to stand for 5 minutes. Serve warm or at room temperature.