10 pitted prunes
1 cup chicken stock
1 Tbsp minced shallots
gray salt
2 lbs. Yukon Gold potatoes
6 Tbsp clarified butter, melted  (1 lb. butter will make 1.5 cups of clarified butter)
Kosher salt and freshly ground pepper

Place the prunes and chicken stock in a small saucepan. The prunes should be just covered with liquid. Bring to a simmer and cook for about 20 minutes, or until the liquid has evaporated and the prunes are very soft. Remove the prunes to a cutting board and finely chop them. Add the shallots and gray salt to taste.

Preheat the oven to 450 F.

Peel the potatoes and trim into cylinders that are 1.5 to 2 inches in diameter. Using a mandoline, cut the potatoes crosswise into 1/16-inch slices. Place the slices in a bowl of cold water for a minute to remove some of the starch, then drain and dry the slices on paper towels.

Put 2 tablespoons of the clarified butter in an 8-inch ovenproof nonstick skillet. Place a slice of potato in the center of the pan. Lay more potato slices around the edge of the pan, overlapping them by half, until you have completely circled the pan. Continue with another overlapping circle of potatoes inside the first. When the entire bottom of the pan is covered, sprinkle a little kosher salt and pepper over the potatoes and repeat the process to form a second layer. Spread half of the prune mixture over the potatoes, leaving a 1/2-inch border all around. Work carefully to avoid moving the potatoes around too much. Make another two layers of potatoes, seasoning the first layer with salt and papper, and spread the remaining prune mixture over them, again leaving a border. Cover the prunes with a final two layers of seasoned potatoes.

Pour the remaining 1/4 cup clarified butter over the potatoes and place the skillet over medium-low heat. Once the butter begins to bubble, cook for 3 to 4 minutes, shaking the pan occasionally to be sure that the potatoes are not sticking. Use a spoon to gently shape the top and sides of the potato cake, keeping the prune filling from leaking out. Transfer the pan to the over and bake for about 30 minutes, or until the potatoes are well browned and crisp. Invert the potato cake onto a board or serving platter. The potato cake can be made a few hours ahead and set aside at room temperature in the skillet. Reheat in a 450 F oven for about 10 minutes, or until sizzling hot.