Preheat your oven to 400°F (200°C). Lightly grease a standard 12-cup muffin tin.
In a small bowl, combine the melted butter, minced garlic, thyme leaves, salt, and pepper. Mix well.
Place the thinly sliced potatoes in a large bowl. Pour the garlic butter mixture over the potatoes and toss gently until all slices are evenly coated.
Take about 4 to 5 potato slices and layer them inside each muffin cup, slightly overlapping them to create a stack shape that reaches the top of the tin. Press the layers down gently.
Sprinkle about 1 teaspoon of the grated Parmesan cheese over the top of each potato stack.
Bake for 35 to 45 minutes, or until the edges are golden brown and crisp and the potatoes are tender when pierced with a fork.
Let the stacks cool in the muffin tin for 5 minutes before carefully removing them with a small offset spatula or knife. Serve immediately.
Notes
Use a mandoline slicer to get uniform, thin potato slices for even cooking and stacking.
Yukon Gold potatoes work best because they hold their shape well during baking.
For extra crispiness, you can brush the tops with a little extra melted butter halfway through baking.