Heat oven to 400°F.
Line a baking sheet with 2 layers of paper towels or a flour sack dishtowel. Have extra paper towels or flour sack dishtowels available.
Peel and slice one potato into ⅛" to 1/16" slices. Lay the slices in a single flat layer on the lined baking sheet and cover with more paper towels or dishtowel. Continue with the rest of the potatoes until all the potatoes are sliced and drying on the towels. Cover the last layer with toweling. See Gr8 Tip.
Heat 2 Tablespoons of the clarified butter in the bottom of your skillet over medium-low heat.
Starting in the middle of pan lay one slice of potato. Then continue making circles of potato slices around the center slice. Slightly overlap each slice so you can't see the bottom of the pan.
When you've finished with the first layer. Brush on some of the clarified butter then lightly sprinkle with salt and pepper.
Make a second layer the same as the first, then butter, salt and pepper. Continue making the layers until all the potatoes are used up.
As you are creating the layers, shake the pan slightly to ensure that the potatoes are not sticking to the bottom. This is important!°
When all the potatoes are layered, butter a piece of foil and lay on top of pan. Put a slightly smaller, heavy pan on top of the foil and press down to compact the "cake."
Remove the heavy pan and foil, cover and place the skillet of potatoes on a baking sheet in the oven for 20 minutes. (The baking sheet will catch any butter that spatters from the pan.) If your pan doesn't have a lid, use foil.
Uncover and cook for 20 to 25 more minutes, or until potatoes are tender and golden brown.
Carefully drain off any excess butter.
Run a thin spatula between the edge of the potatoes and the pan to loosen, then slide the spatula under the potatoes to make sure they are loose.
Lay a serving plate upside down on top of the skillet and very carefully flip the potatoes onto the platter. Careful, it's hot!
If any pieces of potato stick to the bottom of the pan, scrape them up and lay them on top of the cake. If your potatoes don't come out looking nice, you can use Julia Child's trick below.