Using a Mandoline, thinly slice the potatoes. Starting with the smaller pieces, layer a potato slice in the bottom of each of the 8 muffin cups, and brush each potato slice with a thin layer of oil. Lay another slice of potato into each tin, and brush with oil. At every third layer, sprinkle with a little salt and pepper. Repeat stacking, brushing with oil, and seasoning until you have used up the potato slices. At the top of each stack, season with salt and pepper, and sprinkle with fresh thyme leaves.