Place the milk and the garlic in a large heavy saucepan. Season with salt, pepper and a little nutmeg. Bring to boil, and simmer for 15 minutes. Pre-heat oven to 450 degrees.
Peel the potatoes and slice thinly on a mandoline or plastic vegetable slicer. Place potato slices in hot simmering milk and cook very gently for 10 minutes or so, or just until the potatoes begin to soften.
Immediately drain the potatoes in a colander (reserve milk for another use, if desired). Butter an oval gratin dish that measures about 12" long and 10" wide (at the widest spot). Place half the potato slices in the dish, neatly arranged, making sure to sprinkle every single layer of potatoes with a little salt, pepper and nutmeg. When half the potatoes are placed, cover with half of the grated cheese, evenly spread out. Place the second half of the potato slices in the gratin dish, again seasoning with salt, pepper and nutmeg. Top with the remaining half of the cheese, evenly spread out. Pour the cream over and around the potatoes.
Cover the gratin loosely (with a lid or with aluminum foil). Place in the oven, and cook for about 45 minutes, or until the cream has cooked away. Remove the lid and place the gratin briefly under the broiler until brown and bubbly. Serve immediately.