For the gnocchi, pare and steam the potatoes until they are fork tender. Puree.
Blend the cheeses together.
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.
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.
Start a large kettle of salted water to a rolling boil. While waiting on the water to boil, begin the mornay sauce.
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.
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.