Preheat oven to 350°F/180°C.
Butter a 4- or 5-c. shallow casserole dish and then rub the smashed garlic along the bottom and sides.
Carefully lay the potatoes into the casserole overlapping the slices creating a layer. Put down a layer of the cheese and another layer of potato until the potato and cheese are used.
Pour the heavy cream and milk over the potatoes. Season with salt and pepper to taste. Sprinkle any remaining cheese on top of the potatoes.
Bake uncovered for 45 - 50 minutes.