Step 1

Heat the oven. Arrange a rack in the top third of the oven and heat the oven to 425ºF.

Step 2

Peel and slice the potatoes. Peel 2 pounds Yukon Gold potatoes. Cut crosswise into 1/8-inch thick rounds with a mandoline or with a sharp knife. Divide the slices into 4 equal piles.

Step 3

Grease the pan and foil. Melt 3 tablespoons unsalted butter in the microwave, about 30 seconds on high. (Alternatively, melt on the stovetop.) Brush the bottom and sides of an oven-safe 10-inch nonstick frying pan with 1 tablespoon of the butter and sprinkle with 1/4 teaspoon of the kosher salt. Brush a thin layer of butter onto a sheet of aluminum foil big enough to cover the pan.

Step 4

Build the first layer. Starting in the center and overlapping the slices by about half, arrange one pile of the slices in a spiral pattern, making sure the bottom is completely and evenly covered. Use smaller slices in the center and larger slices on the edges. Brush with 1/2 tablespoon of the melted butter and sprinkle with 1/4 teaspoon of the kosher salt.

Step 5

Build the second layer. This time working your way from the outside in to the center (again using the larger slices on the edges), arrange the second pile of potato slices to build the second layer. Brush with 1/2 tablespoon of the butter and sprinkle with 1/4 teaspoon of the kosher salt.

Step 6

Build the last two layers. Repeat arranging the third layer, working from the inside out, then buttering and seasoning. Build the fourth and final layer of potatoes from the outside in. Brush all the remaining butter onto the top layer and season with the remaining 1/4 teaspoon kosher salt.

Step 7

Press and bake for 25 minutes. Place the foil butter-side down onto the potatoes, then weigh down the foil by topping it with a 9-inch cake pan or pie plate. Fill the cake pan or pie plate with pie weights. Bake for 25 minutes.

Step 8

Uncover and finish baking. Remove the weights and foil. Bake uncovered until knife-tender and the bottom is golden brown, about 20 minutes more.

Step 9

Broil the top. Turn the oven to broil on high. Broil until the top is golden brown, about 5 minutes.

Step 10

Unmold and serve. Gently shake the pan to see if the potato cake slides around easily. If it doesn’t, run a thin knife around the edges and slide the spatula underneath the potato cake to loosen. Invert a cutting board over the pan. Grasping both the board and the pan (careful, hot!), flip over and remove the pan. Cut the potato cake into wedges.