This is called a cake as by cooking it in a cast iron fry pan, it comes out round in shape, you can cut it into pieces, like a cake, and it looks great on the plate.
2 tablespoons unsalted butter, melted
1 tablespoon extra-virgin olive oil
1 lb yellow-fleshed potatoes such as Yukon Gold
3/4 teaspoon salt
1/4 teaspoon black pepper
1/2 oz finely grated Parmigiano-Reggiano (1/4 cup)
Put oven rack in middle position and preheat oven to 450°F.
Stir together butter and oil.
Peel potatoes, then thinly slice and toss with 2 tablespoons butter mixture, salt, and pepper.
Heat remaining butter mixture in a 10-inch heavy ovenproof nonstick skillet over moderately high heat. Spread one third of potatoes evenly in skillet. Toss remaining potatoes with cheese and spread evenly over first layer of potatoes in skillet, pressing with a spatula. Cook 3 minutes, then transfer skillet to oven and roast, uncovered, pressing top occasionally with spatula, until potatoes are tender and top is starting to brown, 20 to 25 minutes.
Invert potato cake onto a cutting board and cut into wedges. Makes 4 side-dish servings.