Place the potato, carrot, onion, turmeric, and garlic in a medium-sized pot, cover with 2 cups of water, and place lid on the pot. Bring just to a light boil, lower the heat, and simmer with the lid on until the veggies are fork-tender - about 20 minutes.
Follow the manufacturer's instructions to cook as much pasta as you'd like. Serving guidance can be found on the label. Drain and set aside once it's ready.
Remove your cooked veggies from the heat and set aside to cool for about 10 minutes. Then carefully add everything from the veggie pot, including the remaining water, to your blender. Drain the cashews (discard the water) and add the cashews to the blender, along with the nutritional yeast, apple cider vinegar, salt, and the remaining ½ cup of water. Blend until the sauce is creamy and smooth, about 2 minutes.
Return your pasta to its pot and place it over very low heat. Pour as much cheesy sauce over the pasta as you like and stir to coat everything. Add black pepper to taste.
Dish up and serve!