In a good quality blender that can handle hot food, add cooked potatoes and carrots.
Add 1/2 c cooking liquid to the blender. Blend until smooth.
Add silken tofu, and lemon juice. Blend until smooth.
Add nutritional yeast, garlic and onion powder and salt.
In a medium saucepan over low heat, add 1/2 c water and 1 Tbsp agar powder. Whisk together and do not touch for 3 minutes. DO NOT TOUCH IT!
After three minutes have passed, whisk the cheese mixture in the blender into to the saucepan, whisking as you pour until well incorporated.
In a small bowl, add the 2 Tbsp tapioca starch with 2 Tbsp cold water and whisk with a fork until mixed.
While whisking, add the tapioca mixture into the cheese mixture. Cook for 1-2 minutes until the cheese thickens.
Add the cheese sauce to the cooked pasta and mix well!
Serve immediately or store for later in the fridge!