Place all ingredients into the bottom of a 6-quart slow cooker.
Cover with the lid and cook on LOW setting for 2 to 3 hours.
Use an immersion blender to break up blueberries into a puree (or you can alternately transfer them to a food processor or blender). If using a cinnamon stick, set it to the side while blending and then return it to the pot.
Continue cooking, with the lid offset to create a vent, for 6 to 8 additional hours.
Stir the blueberry butter once an hour and check the progress.
Blueberry butter is done when it is thick and has the desired consistency.
Remove and discard the cinnamon stick and transfer the blueberry butter to sterile canning jars and cover with lids. Allow to cool to room temperature.
Store sealed jars in the refrigerator for up to 3 weeks or in the freezer for up to 1 year.
