Place all the ingredients except the two extra candy canes in a blender and blend until smooth. If you have ice cream maker continue to make the ice cream according to the manufacturer's instruction. If no ice cream maker then continue to step 3.
Empty the liquid in a freezer safe container. Crush the two candy canes and fold them in. Cover with a lid and freeze for 6 hours or overnight.
After the 6 hours, take out the ice cream, let it soften a little bit. Then break into big chinks and place in a food processor and chop further until smooth. Then pour the ice cream mixture back in the container, cover and freeze again. Repeat this step 3 to 4 times every hour, for soft serve ice cream.
Serve with some crushed candy canes sprinkled on top.