Peel the potatoes and grate them on a box grater. Wrap the grated potatoes in a kitchen towel and squeeze out as much liquid as possible. Combine the potatoes in a bowl with the egg, flour, salt and pepper. Mix well.
Melt the clarified butter in a large saute pan over medium heat. Place a tablespoon of the potato mixture into the sizzling butter and cook for 2 minutes. Turn the pancakes over and cook for another 2 minutes, or until crisp on the outside and golden brown. Serve the pancakes hot from the skillet.
Note: To make the clarified butter, slowly melt 4 tablespoons butter in a small saucepan. Set it aside until the milk solids settle. Spoon off any solids that rise, then carefully pour off the golden liquid, discarding the milky part in the bottom of the pan.