Apple Cider and Apple Cider Vinegar give the cabbage a nice apple flavor.
Melt butter in large pot over medium-high heat. Add onion; sauté until beginning to soften, about 5 minutes. Add cabbage; saute; acute; until slightly wilted, tossing frequently, about 6 minutes.
Stir in apple cider. Reduce heat to medium; cover and cook until cabbage is tender, stirring occasionally, about 6 minutes. Uncover; simmer until almost all liquid in pot evaporates, about 3 minutes. Stir in vinegar. Season with salt and pepper.