Add onions, potatoes, whole garlic cloves and enough water to just cover them to a sauce pan and bring to a boil. Cover the pan and simmer for 15 minutes, or until vegetables are very soft.
While the vegetables are simmering, cook the pasta. Drain pasta (do not rinse) and set aside with the lid on to keep pasta warm.
Place the non-dairy milk, cashews, salt, nutritional yeast, coconut oil, lemon juice and black pepper in the cup of your blender. Drain water from softened vegetables and add to blender; process until perfectly smooth (use Soup button if you have a Blendtec).
In a large bowl, toss the cooked pasta and blended alfredo sauce until completely coated. Serve immediately with steamed or roasted broccoli or asparagus.