Preheat the oven to 175°C. Rub the garlic around the inside of an 8 by 8 by 2-inch casserole dish and let it dry. Reserve the remaining garlic. Rub the butter around the inside of the dish. Reserve the remaining butter.
Peel and thinly slice the potatoes on a mandoline or vegetable slicer (about 1/8-inch-thick slices).
In a medium saucepan, combine the garlic, butter, potatoes, half-and-half, salt, pepper to taste, and nutmeg. Bring to a boil, lower the heat to medium-high, and cook, stirring, until the mixture has thickened, about 5 minutes. Transfer the mixture to the prepared dish. Shake the pan so the potatoes are distributed evenly.
Bake the potatoes, basting occasionally, until lightly browned and bubbly, about 1 hour. Remove from the oven and let cool for 10 minutes before serving.