Place apples in the bottom of a 6 quart slow cooker.
In a mixing bowl, combine the brown sugar, granulated sugar, cinnamon, cloves, and salt. Pour the mixture over the apples and stir until well combined.
Place the lid on the slow cooker and turn the heat on low. Cook for 10 hours, stirring occasionally.
Remove lid and use an immersion blender to puree apples until completely smooth. (If you don't have an immersion blender, place mixture in a blender, puree, and return mixture to slow cooker.)
Continue cooking uncovered on low, stirring occasionally, for an additional 1-2 hours until desired consistency is reached. Apple butter will continue to thicken upon cooling.
Transfer to an airtight container or individual airtight containers. Store in refrigerator for up to 2 weeks.