Using a mandoline (or a sharp chef’s knife and mad knife skills), slice the potatoes ⅛ inch (3 mm) thick.
In a 10-inch (25-cm) skillet or sauté pan, heat 1 tablespoon of the ghee over medium-high heat. When it shimmers, quickly and carefully add the potato slices in fairly even layers, sprinkling each layer with a pinch of salt and a grinding of pepper. Cover the skillet, lower the heat to medium, and cook the potatoes without disturbing them for 10 minutes. Lift the lid and slide a thin metal spatula underneath to check the level of browning; if the potatoes on the bottom are deeply browned, lower the heat to medium-low, cover, and cook for 10 minutes longer, or until the potatoes on the top layer are tender. (If the potatoes are not yet deeply browned, cook for 5 more minutes on medium, then lower the heat and cook for 5 minutes.)
Using the spatula, lift big sections of the potatoes and turn them over so the browned potatoes are on top. Dollop the remaining 1 tablespoon ghee in between the sections, shaking the pan to get it underneath. Raise the heat to medium-high and cook, uncovered, for about 5 minutes longer, until the bottom layer is nicely browned. Serve.