Wash cranberries and discard any shriveled or bruised berries. Pour into food processor bowl.
Juice one orange and add juice to cranberries in food processor, along with honey, ginger, and cardamom if using.
Process until the mixture looks the way you want. It can be more chunky or more smooth.
Scoop cranberry sauce into 2 pint jars, filling them to within one inch of the top. Set aside at room temperature to ferment.
Each day, remove the lids to release pressure. You don't want the jars to explode! You will see bubbles from on top. After 2-3 days (or longer), put your jars in the refrigerator to stop (mostly) the ferment. If you aren't sure when to stop, taste a tiny bit. It will be more sour and the berries will be softer as it ferments. It is up to your taste!
Store your jars for several weeks (maybe more) in the refrigerator or other cold place. Before serving, check to see if there is more liquid than you want and drain the excess. Scoop into a glass or crystal serving dish to make a pretty dish on your table!