
Heat the oven to 400°F (200°C) with a rack in the middle, then brush the 12 cups of a standard muffin tin with 1 tbsp of the melted butter.
Slice the unpeeled potatoes 1/16 inch (2 mm) thick on a mandoline, without rinsing them, until you have a bowl of even rounds.
Toss the slices with the remaining 5 tbsp butter, the salt, pepper and garlic powder until every slice glistens.
Add the Parmesan and toss again until the slices are lightly coated, with no dry patches.
Stack the slices into the cups, sprinkling about 2/3 cup of the cheddar between the layers, until each stack stands about 1/2 inch (1 cm) above the rim, then press down gently.
Bake 30 minutes, until the edges are golden and the tops start to curl and crisp.
Sprinkle the remaining cheddar over the stacks and bake 8 to 12 minutes more, until the cheese bubbles, the rims are deep amber and a paring knife slides through the center with no resistance.
Cool in the pan 5 minutes, run a thin knife around each cup and lift the stacks out gently with a spoon or small spatula.
Approximate values per serving.
Recipe from Home Recipes: https://www.hmrecipes.com/cheesy-potato-stacks/