Prepare potatoes and carrots and place in a medium-sized pot on the stove. Cover with water and bring to a boil. Boil until soft, about 8-10 minutes.
Drain potatoes and carrots into a bowl. Save the liquid you drain off. Transfer potatoes and carrots to the blender, and add back 2/3 cup of the liquid from cooking (add more water if needed to make 2/3 total).
Blend all ingredients on high until the cheese sauce is extremely smooth, about one minute. May need to scrape the blender down if not using a VitaMix. A VitaMix blender will do a wonderful job making this cheese perfectly smooth.
Store in the refrigerator up to a week. May need to add some water to the cheese after taking it out of the refrigerator if the cheese has become thick.
You can also freeze this cheese, but make sure to reheat it until it's HOT when using again. Getting it hot will restore the smooth texture.