Core and chop the apples into small pieces, about ¼ inch each. Place them in the basin of a large slow cooker.
In a medium-sized bowl, mix the brown sugar, granulated sugar, cinnamon, salt, and ground cloves until well combined.
Pour the sugar mixture over the apples and stir until they are well coated.
Cover the slow cooker and cook on low heat for 10 hours.
After 10 hours, use an immersion blender to puree the apples until smooth.
Scrape the inside of the vanilla bean into the apple puree (or add vanilla extract) and stir thoroughly.
Cook uncovered on low heat for an additional 2 hours, stirring occasionally to reach the desired thickness.
Store the apple butter in an airtight container in the refrigerator for about 2 weeks, or freeze for several months.