Add potatoes and carrots to a pot of water. Bring to a boil, and let boil for 10 minutes, or until potatoes and carrots are soft. Strain and add to a blender.
Add all remaining ingredients to the blender and blend until super creamy and smooth.
Pour the nacho cheese into a pot and heat on medium-low heat until it starts to bubble. This will activate the cornstarch and help thicken the nacho cheese.
Serve warm with your favorite chips!
This recipe makes about 2.5 cups of nacho cheese.The original recipe included vegetable stock, but I don't think it really added much to the recipe so it was replaced with more non-dairy milk. You can use half milk/half stock if desired.