Preheat oven to 350 °F and spray muffin tin with oil. Set aside.
Peel potatoes and cut into cylinders that will fit in the muffin tin. To do so, stand each potato up and shave off corners with a knife.
Slice potatoes thinly with a knife or use a mandolin set to slice 1mm.
Slice potatoes thinly with a knife or use a mandolin set to slice 1mm.
Place potato slices into muffin tin so that they go halfway up.
Pour 1 teaspoon of the butter mixture on top with 1 teaspoon of asiago. Fill the muffin tin up to the top with more potato slices. Pour the rest of the butter mixture on top and cover with aluminum foil before placing in oven.
Bake for 40 minutes before removing aluminum foil and topping with parmesan.
Bake for 10 more minutes before removing from oven and serving.