Put all ingredients with 3/4 cup water in a medium saucepan. Simmer over low heat, stirring often, until most of the cranberries have popped and apples are tender, 10 to 15 minutes. Remove cinnamon stick and add sugar and salt to taste.
Make ahead: Up to 1 week, chilled.
*Crush with the bottom of a thick water glass or a small saucepan.