Using a food processor, chop cabbage, pulsing until finely chopped. It might be helpful to work in small batches to make sure the cabbage isn’t pulverized but just chopped up into small squares. The same can be done with the carrot. Place cabbage and carrot in a medium bowl.
In a separate small bowl, combine the rest of the ingredients. Mix until smooth. Pour over cabbage/carrot mixture and stir. Don’t be concerned if it seems a bit dry at first. The moisture from the cabbage will be drawn out before too long.
Refrigerate for at least 30 minutes before serving. This allows for the dressing as well as the moisture from the cabbage to meld well. Stir before serving.