Step 1Put a rack in the middle of the oven and heat the oven to 400 degrees. Generously butter a 2 1/2 - to 3-quart gratin dish or other shallow baking dish.
Step 2Peel the potatoes. Cut them crosswise into one-sixteenth-inch-thick slices with a slicer and transfer them to a 4-quart heavy saucepan. Add the half-and-half, garlic, salt and pepper and bring just to a boil over moderate heat.
Step 3Pour the potato mixture into the buttered dish, distributing the potatoes evenly. Sprinkle nutmeg and cheese evenly over the top. Bake until the potatoes are tender and the top is golden brown, 35 to 45 minutes. Let stand for 15 minutes before serving. (The gratin can be made up to 1 day ahead. Cool completely, then refrigerate, covered. Bring to room temperature before reheating, covered, in a 350-degree oven.)