Preheat oven to 350 degrees F. Using a pastry brush, lightly brush 8 muffin tin cups with oil.
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.
Bake for 35-45 minutes or until the potatoes are golden brown and cooked through. Garnish with additional fresh thyme leaves as desired.
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