Bring 4-5 cups of water to a boil in a medium sauce pan.
Add potatoes, carrots and onions.
Bring back to a boil and reduce heat to low until vegetables are tender.
Drain water, reserving liquid, and add vegetables to Vitamix.
Add 3 cups of reserved water, cashews, coconut milk, nutritional yeast, lemon juice, garlic powder, salt and cayenne pepper to Vitamix.
Blend on high until ingredients are nice and creamy, less than a minute.
In the buttered 9 x 13 baking dish, add a ladle of cheese sauce to the bottom of the pan.
Add a layer of potatoes, cheese sauce and lightly sprinkle with cayenne pepper and pepper.
Add the remainder of butter, sliced, in between one of the layers of potatoes.
Repeat until your baking dish is full.
Cover with foil and cook for 1 hour, or until the potatoes are tender.