In a large saute pan, heat the olive oil and saute the red onions with the apples until they are slightly golden, about 5 minutes. Add the red cabbage, season with salt and saute until the cabbage begins to wilt, 5 to 10 minutes. Add the cranberries, sugar and vinegar and cook until the juices reduce and the cabbage looks glossy, about 15 minutes. Chill the cabbage and cranberry mixture overnight. It can be served both warm or cool, according to one's taste.
Recipe courtesy Erin Zircher, The Boarding House, Nantucket, MA