Peel and wash the potatoes. Cut them into very thin slices using a potato slicer.
Grate the Parmesan cheese and add it to the potatoes. Season with salt, pepper, garlic, and thyme. Add the rest of the melted butter and mix everything together thoroughly.
Grease 12 muffin molds with half of the butter. Stack the potato slices into the muffin molds on top of each other.
Bake the potato stacks at 375°F for about 50 minutes in a preheated oven. Allow the stacks to cool for a few minutes and then gently remove them from the muffin pan with a knife. Serve and sprinkle a little Parmesan on top.