Preheat oven to 375ºF. Rub an earthenware gratin dish (I used a 9x13-inch Pyrex) with smashed peeled garlic and butter. Using a mandoline or knife, cut potatoes 1/8-inch thick and layer overlapping slices in the prepared pan. Season with salt (don't be afraid to use a heavier hand with the salt — potatoes can handle it), pepper, and thyme leaves (no need to chop — just pull and scatter). Lightly grate nutmeg over top — be sure to go light. Make another layer of potato slices and season again in the same manner. Moisten with cream, cream and chicken stock, or milk to the top level of the top layer of potatoes. (I used 1.5 cups each of heavy cream and chicken stock, but I probably could have used more, and you may need more or less depending on the size of the pan you are using.) Sprinkle the top with grated cheeses, and distribute thin shavings of butter (forgot to do this) on top. Bake 45 minutes to 1 hour, checking after 40 minutes or so to make sure the potatoes are not browning too quickly. If they are browning too quickly, cover the pan with foil and continue baking until the potatoes are tender and the top is nicely browned. You can also turn the temperature down to 350ºF if necessary.