Start by preheating your oven to a toasty 400°F. While it's warming up, generously grease your muffin tin with cooking spray or butter.
Grab your trusty mandoline slicer and carefully slice the unpeeled potatoes into whisper-thin rounds, about 1/16 inches thick. The mandoline is your best friend here for even slices. In a large mixing bowl, toss the potato slices with the melted butter, grated Parmesan cheese, fresh thyme leaves, garlic powder, salt, and pepper.
Neatly stack the seasoned potato slices into the prepared muffin tin. Remember, they'll shrink down as they bake, so don't be shy—pile them a little higher than the rim. Bake for 40-45 minutes. You're looking for those edges to be crisped to perfection.
Let the potato stacks cool in the pan for about 5 minutes—this makes them easier to remove.
Remove the stacks, garnish with a sprinkle of fresh thyme.