Melt the butter in a large skillet over medium heat. Add the cabbage and onion, and cook until the onion is soft, about 5 minutes.
Stir in water, vinegar, sugar, caraway seeds, and salt. Reduce the heat to low, cover the skillet, and cook, stirring occasionally, until the cabbage is tender, about 20-25 minutes.
During the last couple of minutes, increase the heat to medium and add the garlic. Remove from heat when garlic is cooked. If desired, drizzle with aged balsamic vinegar and sprinkle with parsley when serving.