1/2 lb unsalted butter
3 lbs of potatoes
Salt, pepper 

• Preheat oven to 450°F.
• Set one rack in very bottom level, and another just above it.
• Clarify the butter: melt it, skim off scum, and spoon the clear liquid butter off the milky residue.
• Peel the potatoes, trim into cylinders to have uniform slices. Do not wash potatoes after peeling.
• Slice cylinders into even rounds 1/8 inch thick (about 8 cups).
• Dry thoroughly in paper towels.
• Pour 1/4 inch of clarified butter into the pan and set over moderate heat.
• When hot, start rapidly arranging the first layer of potatoes in the bottom of the pan.
• Starting with one potato slice at the center of the pan, overlap a circle of potato slices around it.
• Overlapping in the other direction, arrange a second circle around the first, and so on until you reach the edge of the pan.
• Pour on a spoonful of clarified butter, salt and pepper.
• Starting at the circumference of pan and reversing direction again, arrange another layer of potato all the way to the center.
• Continue filling the pan in that fashion, filling completely and allowing the potatoes to form a 1/4 to 1/2 inch dome in the center.
• You should have enough butter so that it bubbles up the sides of the pan.
• Butter the bottom of a heavy saucepan and press it hard on the potatoes, forcing the layers together.
• Butter the underside of a cover, place it on the pan of potatoes and cook in the oven for 20 minutes.  Put a pan under the potato pan to catch any dripping butter.
• After 20 minutes, uncover, press the potatoes down hard again and continue baking 20 to 25 minutes more, uncovered.
• Press down hard again just before the end of cooking.
• Gently draw an edge of the potatoes  away from side of dish to verify that it is brown and crusty. Bake more if necessary.
• Drain out excess butter.
• Shake pan gently to make sure potatoes are not stuck to bottom, run a spatula gently to loosen them if necessary.
• Invert a serving dish over the potato pan, reverse the two, and potatoes will fall into the dish.
• They should look like a brown cake.
• To keep the cake for at least half hour before serving time, cover loosely with foil and set in 120°F oven.