In a medium pot boil the carrots, cashews, and potatoes for 30 minutes or until the potatoes are fork tender. Drain when they are done.
Once the potatoes are done preheat the oven to 400°F (204°C).
In a blender add the carrots, cashews, and potatoes along with the seasonings, nutritional yeast, and non-dairy milk. Blend for 1 to 2 minutes in a high speed blender until smooth and creamy.
Bring a medium pot of salted water to a boil and cook your pasta for 5 minutes (or 5 minutes less than the box tells you to). It should be softer on the outside but harder on the inside. If you are using smaller pasta like elbows check it after 2 minutes.
Meanwhile in a separate larger pot pour in the cheese sauce, add in 1 slice of vegan American cheese, add in ⅔ of the vegan cheddar shreds and vegan mozzarella shreds (I save ⅓ for topping). Fill the blender up with ¼ cup (60ml) water and swish it around to get the remaining cheese sauce and pour into the pot. Cook over medium low heat for 5 minutes until the vegan cheese starts to melt, it doesn't need to be melted all the way.
When the pasta is done reserve ¼ cup (60ml) of pasta water and drain the pasta. Pour the pasta in along with the pasta water to the vegan cheese sauce. Mix together until well coated. The sauce should be thinner and runnier than you think because as it bakes it will thicken. Taste an add any extra seasonings.
Pour into a small baking dish (7 inches x 6.5 inches) and top with the remaining vegan cheese. If you want it to be cheesier feel free to add more vegan cheese on top/
Cover with foil leaving it slightly vented so the vegan cheese doesn't stick to the top as it melts. Bake for 40 minutes covered and then broil over low for 5 to 7 minutes uncovered.
This is best when enjoyed immediately.