Prepare the Garlic Cashew Cheese Sauce, followed by the Vegan Parmesan (I like to make the parm quite coarse in texture to give this recipe some crunch). Set aside.
Preheat the oven to 425°F (220°C). Liberally oil a 9 by 13-inch (3 L) casserole dish, making sure to coat the sides and bottom completely.
Using a mandoline, slice the peeled potatoes into very thin (less than ⅛-inch-thick/2 mm) slices (no thicker, or they’ll take a long time to cook through).
Spread a single layer of sliced potatoes over the bottom of the casserole dish, just barely overlapping them by about ⅛ inch (3 mm) and covering the bottom of the dish. Sprinkle a small pinch of salt over the sliced potatoes. Pour a scant 1 cup of the cashew cheese sauce over the potatoes so it covers the potatoes’ surface completely (you can use the measuring cup or your fingers to help spread the sauce over all the potatoes). The sauce will look very thin and watery, but don’t worry, because it thickens while baking. Repeat this layering process (remembering to lightly salt each layer of potatoes) until you have used all the sauce and sliced potatoes. (There should be five layers if you use a 9 by 13-inch/3 L casserole and your potato slices are less than ⅛ inch/2 mm thick.) Make sure your final layer is sauce, and use all the remaining cheese sauce on this final layer. It will look like a swimming pool of sauce, but this is normal and it will firm up as it bakes.
Sprinkle all the parmesan over the sauce. Cover the casserole dish with aluminum foil. Using a sharp knife, cut about four 1-inch (2.5 cm) slits into the foil to vent steam.
Bake the casserole for 1 hour. After 1 hour, remove the foil and check for doneness by sliding a knife into the center of the casserole. You are looking for no resistance when you insert the knife (if your potatoes were sliced thicker than ⅛ inch/3 mm, the casserole may take longer to bake). If there is resistance to the knife, replace the foil and bake for 5 to 15 minutes more, then test again.
Serve with a sprinkling of thyme leaves, if desired, and prepare to fall into a heavenly trance while enjoying each and every bite!