Peel, core, and finely chop the apples.
Add the apples to the crock of a 6-quart slow cooker. Add the sugars, cinnamon, cloves, and salt. Mix well. Cover and cook on high for 1 hour, then reduce the heat to low and cook for 10 hours, stirring occasionally.
Uncover and and stir well. It should be thick and dark brown. If you prefer a smoother apple butter, you can use an immersion blender to puree the mixture. Leave the lid off and cook for an additional hour on low to allow the mixture to thicken even more.
To store, allow the apple butter to cool, then place in sealable containers or jars and refrigerate for a few weeks or freeze for even longer.