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preheat oven and a shallow ovenproof baking dish or cast-iron skillet to 400° f.
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in a large pot of boiling, salted water, cook pasta to al dente.
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strain but do not rinse.
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simultaneously, in 2-quart, heavy-bottomed stockpot, whisk butter and flour together over medium heat to make a blonde roux.
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add milk and heavy cream; whisk until boiling.
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add all the cheese, reserving ½ cup of parmigiano reggiano; stir until mixture is melted evenly throughout.
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add cooked pasta to cheese mixture, season to taste with kosher salt and freshly ground black pepper.
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remove hot baking dish from oven and butter it evenly while hot.
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add entire contents to buttered baking dish, sprinkle top with reserved parmigiano reggiano.
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bake in the middle of the oven for 25 minutes, until top is browned.
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serve immediately.