Preheat the oven to 425°F (218°C) and brush a roughly 10" (25.5cm) square piece of aluminum foil with the olive oil.
Cut the top quarter off each garlic head with a sharp knife so the cloves inside are exposed. Then place the largest parts, cut side down, in the middle of the foil. Draw the foil up around them. Wrap and squeeze it tightly shut. Separately wrap the little pieces you cut off the top, too, and store in the fridge for another recipe.
Place the foil-wrapped garlic heads in the oven, directly on the oven shelf, and roast for about 40 minutes. Check whether they feel a little squishy through the foil. Return them to the oven for a few more minutes if not. If they are done, remove and set aside until cool enough to handle.
The garlic can be roasted in this way up to 4 to 5 days before you make the Alfredo and then stored in the fridge. I like to do it when I have the oven on to cook something else.
Make the sauce by opening the foil wrapping and squeezing the garlic cloves out of their silvery, papery skins from the root end, straight into your blender. They will pop out really easily.
Add the cashews, almonds, nutritional yeast, nondairy milk, lemon juice, vinegar, pepper and 1 teaspoon of the salt; then blend until completely smooth. Taste to check the seasoning and add more salt, if necessary
Bring a large pot of water to a rolling boil. Season with the remaining teaspoon of salt, add the fettuccine and cook for the time directed on the package. It usually takes around 8 minutes.
When it’s done, scoop out about 1/2 cup (120 ml) of the boiling water and set aside before draining the fettuccine.
Return the fettuccine to the pot and immediately add the sauce. Return the pot to the stove and allow it to warm through over low heat for 3 to 4 minutes. It will thicken up a little as it warms up and you can loosen it to your liking with the starchy pasta water that you set aside. You won’t need all of it; just add it a little at a time, if necessary. Serve as soon as the sauce has heated through.
Leftover sauce can be reheated. It will thicken up when refrigerated, but just loosen it up with a little nondairy milk, warm through and it will be good as new!