Preheat oven to 375°F (190°C) and grease a 12-cup muffin tin.
In a large bowl, toss sliced potatoes with melted butter (and/or olive oil), Parmesan, garlic powder, salt, and pepper until evenly coated.
Layer the potato slices into each muffin cup, stacking them to the top (they will shrink slightly while baking).
Bake for 45–55 minutes, until the edges are golden and the centers are tender.
Let the stacks rest for 5 minutes, then carefully remove from the muffin tins. Garnish with extra Parmesan, herbs, or salt if you like.