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For the gnocchi, pare and steam the potatoes until they are fork tender. Puree.
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Blend the cheeses together.
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Blend the cheeses, potatoes and eggs together. Add the flour very slowly, mixing in after each addition. You want a very soft dough, not too stiff with flour or the gnocchi will be heavy and tough.
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Knead, creating a soft dough. Mold the dough into teaspoon size pieces. Place on a floured, inverted fork and press slightly. The tines will make ridges to help the sauce cling to the gnocchi.
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Start a large kettle of salted water to a rolling boil. While waiting on the water to boil, begin the mornay sauce.
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Heat the butter in a sauce pan and add the mushrooms, saute until most of the liquid has evaporated. Add the flour and cook 2 minutes over low heat, adding drops of chicken broth as needed to keep from being too dry while cooking. Stir in the chicken broth and half & half. Reduce heat and simmer until thickened. Stir in the cheese and simmer for 2 more minutes. Keep sauce warm over very, very low heat.
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Drop the gnocchi into the salted boiling water. Cook for 3 minutes after the dumplings begin floating. Drain and place in large serving bowl. Top and toss with Mornay Sauce.