In a high speed blender or food processor, combine all ingredients for the ice cream until smooth.
Remove 1/3 cup of the mixture and set aside.
Meanwhile, to make the swirl, combine all ingredients in a high speed blender or food processor until smooth, and set aside until the ice cream is done.
Pour 1/3 of the finished ice cream into a freezer safe container, then drop some of the swirl by the Tbsp over that, as well as the plain mixture, then half the remaining ice cream, then more swirl and plain mixture, then the last of the ice cream and more swirl and plain mixture, and swirl with a knife to marble.
Let chill in the freezer for about 4 hours or overnight until more firm before scooping (if it becomes too hard, let sit out about 15-20 minutes before serving).