Put the potatoes in a large saucepan and cover them generously with cold water. Bring to a boil over medium heat and cook until the potatoes are tender but still a bit firm when pierced with a thin knife, 30 to 35 minutes. Drain the potatoes and let cool slightly.
Preheat the oven to 400 degrees F. Generously butter a large baking dish.
As soon as the potatoes are cool enough to handle, peel them, let cool to room temperature, and then cut them into 1/4-inch rounds.
Layer the potato slices in the baking dish, slightly overlapping them. (The potatoes can be prepared ahead to this point, tightly covered, and refrigerated.) Mix the nutmeg with the milk and pour over the potatoes. Season lightly with salt. Sprinkle generously with Parmigiano and dot with the butter.
Place the baking dish on the middle rack of the oven and bake until the cheese is melted and the potatoes are light golden on top, 15 to 20 minutes. Remove from the oven and let cool for a few minutes. Serve warm or at room temperature.
Recipe courtesy of BIBA'S TASTE OF ITALY (Morrow, 2001) by Biba Caggiano