In a medium saucepan over medium heat, combine the cranberries, sugar and cinnamon stick with 1 cup of water.
When the first berries start to burst, add apple and 2 cups of water. Boil on low for about 10 minutes until apples become soft.
This is important: Take 1/2 cup of liquid out of the pan and add cornstarch to it. Mix. Pour the cornstarch mixture back into the pot and stir.
Take off the heat and cool. The sauce will thicken as it cools. Refrigerate for about 3 hours before serving. (Store in a covered container in the fridge for up to 1 week.)