Preheat your oven to 375 degrees Fahrenheit. Generously grease a standard 12-cup muffin tin with cooking spray or a bit of softened butter to ensure the potato stacks don’t stick to the sides during baking.
Scrub the potatoes clean and leave the skins on for extra texture and nutrition. Using a mandoline slicer or a very sharp knife, cut the potatoes into thin rounds, roughly 1/16th of an inch thick. Consistency is key here to ensure all the layers cook at the same rate.
In a large mixing bowl, combine the potato slices with the melted butter, Parmesan cheese, garlic powder, thyme, salt, and pepper. Use your hands or a large spoon to toss everything together until every single potato slice is well-coated in the herb and butter mixture.
Layer the potato slices into the prepared muffin tin cups. Stack them until they reach slightly above the rim of each cup, as they will shrink down a bit as they roast. Try to place the larger slices at the bottom and the smaller ones on top for a neat, flower-like appearance.
Place the tin in the oven and bake for 45 to 50 minutes. The edges should be a deep golden brown and the centers should be easily pierced with a sharp knife. If the tops are browning too quickly, you can loosely cover the tin with foil for the last 10 minutes.
Remove the tin from the oven and let the potatoes rest for about 5 minutes. This helps the cheese set and makes them easier to remove. Run a small knife or offset spatula around the edges of each stack to pop them out, then garnish with fresh rosemary before serving at your Christmas feast.