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Prepare a shallow 2 quart gratin dish, by thoroughly rubbing with the garlic halves.
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Preheat the oven to 375 degrees.
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In a large saucepan, bring the milk to boil over medium heat. Add the cream and 3/4 of the cheese, stirring to blend.
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Finely chop the garlic used for rubbing the dish and add.
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Season with salt, pepper and a grating of the nutmeg. Add the potatoes and celeriac and mix well with a wooden spoon.
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Cook over low heat, stirring often until the potatoes and celeriac are half way done, about 10-15 minutes.
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Taste for seasoning.
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Transfer the vegetables and their liquid to the prepared baking dish. Sprinkle with remaining cheese and butter.
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Place in the center of the oven and bake until the potatoes and celeriac are cooked through and the top is crisp and golden, about 1 hour and 15 minutes. Serve immediately