Preheat the oven to 350 degrees F.
Peel potatoes and cut diagonally into 1/4-inch thick slices.
In a saucepan combine 3 cups of the half-and-half, garlic, freshly grated nutmeg and salt and pepper, to taste. Bring to a boil over moderate heat.
Butter a 1 1/2 quart oval gratin dish, layer potatoes and cheese (reserving 1/4 cup of the cheese for the topping) and pour the cream mixture over the potatoes. Sprinkle the top of the gratin with the reserved cheese and dot with the butter. Transfer the gratin to the oven and bake for 30 to 40 minutes, or until bubbling and golden. Remove from the oven and let it rest for 5 minutes before serving.