Place apple pieces into a large slow cooker. Add white sugar, brown sugar, salt, cinnamon, nutmeg, allspice, and vinegar. Add water and mix well.
Cover and cook on High until apples are starting to soften and release liquid, 1 to 2 hours. Reduce heat to Low and cook, uncovered, until all the apple flesh is dissolved, 5 to 6 hours. Stir occasionally.
Puree using an immersion blender until smooth. Continue cooking, stirring occasionally, until darkened and thick, about 4 hours more. Pass apple butter through a strainer if desired. Seal in a glass container and refrigerate until cool.
