Wash the apples well, and cut them into large chunks, discarding the core and seeds. Place in a crock pot.
Rinse the cranberries and add them to the crock pot. Stir the fruit mixture.
Cover and cook on HIGH for 4 hours, stirring occasionally to prevent sticking. Add a bit of water if necessary, though the natural juices are usually sufficient.
Puree the softened fruit in a high-speed blender or food processor in two batches.
Push the puree through a mesh strainer with the back of a large spoon, discarding the light layer of solids. Rinse out the strainer between batches.
Return the strained puree to the crock pot. Bury the cinnamon stick in the puree.
Cook on HIGH, uncovered, for another 2 hours, or until the mixture is thick and spreadable, stirring occasionally.
Spoon the thickened fruit butter into clean glass jars. Let cool, then cap and refrigerate. It will keep for 4 weeks in the refrigerator, or up to a year in the freezer.