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1
Preheat the oven to 350.
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2
Make the herb cream: Melt the butter in a small saucepan over medium low heat. Add the anchovy and stir until it breaks down. Add the remaining ingredients and slowly heat until it just starts to bubble. Turn off the heat and let sit for 15 minutes. Remove the onion slice. I then blend with an immersion blender. Alternately, if you prefer not to blend, you can just mince the herbs and garlic before adding to the pot. Set aside.
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3
Saute the mushrooms in a TB of butter over medium high heat for 4-5 minutes until cooked. Season with salt and pepper
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4
Lightly butter a gratin dish.
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5
Using a mandoline, slice the potatoes and turnips 1/8 inch thick. I do this as I assemble the gratin because it is hard to judge how many potatoes and turnips you will end up needing. It is very dependent on the size of your gratin dish.
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6
Place a layer of overlapping potatoes on the bottom of the gratin dish. Lightly sprinkle with salt, pepper, and a scant TB of parmesan. Add a layer of turnips and then sprinkle with more salt, pepper and a scant TB of parmesan. Add another layer of potatoes and repeat with the salt, pepper, and parmesan. Add all the mushrooms in one layer. Top with another layer of potatoes, then turnips, then potatoes, sprinkling each layer with the salt, pepper, and parmesan. Press down firmly to compress the layers.
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7
Top the gratin with the remaining parmesan, if any, and then the gruyere. Take a small paring knife and pierce the grain in a few spots. Then slowly pour in the herb cream, stopping when the cream is just barely to the top layer. You may not need all the cream; again, very dependent on the size of your dish.
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8
Bake for approximately 45 minutes until the potatoes are tender and the top is golden.
