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Rub the smashed garlic all over the inside of a 9X13 gratin or casserole dish (see notes above about broiling). Then rub the tablespoon of butter all of the inside of the dish as well. Set aside.
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Preheat the oven to 325 F.
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Place the onions, minced garlic, heavy cream, salt, pepper and thyme leaves in a medium saucepan. Bring to a boil and then simmer gently for 20 minutes. Do not let it boil hard or you risk the cream breaking.
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Let the cream sauce cool for about 5 minutes when it is done. Transfer it to a blender. Add 8 ounces of shredded gruyère cheese. Leave the hole at the top of the blender lid open, and cover it loosely with a towel. Blend until smooth.
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Fan the potato slices out as in an accordion, tilting up, so that the tops will crisp a bit under the broiler. Fill in any gaps with extra slices of potatoes. Pour the cheese and cream sauce over the potato slices.
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Cover the dish tightly with foil. Bake for 75-80 minutes, or until the potato slices are tender.
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Sprinkle the remaining gruyère and the grated parmesan cheese over the top of the casserole. Place under the broiler, now uncovered, and broil until the top is bubbling, browned and a little crispy, about 5-10 minutes.
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Let stand for 5 minutes before serving.