That's what the stirring is for! I have explained this!
When the mixture starts to freeze around the edges, you scrape the container down and stir it. Wait a little, until more has frozen, and stir it again. Keep stirring every so often, increasing your stir speed as it gets thicker and thicker. This breaks up the ice crystals, giving the finished product a smoother texture. After a while, it will get extremely hard to stir -- like stirring cement by hand. At this point, eat it straight, or just let it firm up some more.