Preheat oven to 350°F.

For pistachio and basil pesto:

Place basil, pistachios and garlic cloves in a food processor; pulse until a rough puree.

Add extra virgin olive oil and continue to pulse until oil, basil and pistachios have all combined into a smooth puree.  Transfer sauce to a large work bowl; fold in cheese and season to taste with salt and pepper.  Set aside.

For potato gnocchi:

Brush each potato lightly with extra virgin olive oil.

Wrap each potato in aluminum foil and bake in oven until tender, for about one hour.

When potatoes are cool enough to handle, peel and pass them through a food mill or potato ricer which yields about 3 cups of sieved potatoes.  On a clean work surface, mound sieved potatoes with a well in the middle.  In the well place egg yolks, 2 cups of flour and salt.

Mix all the ingredients together and make sure to dust work surface with additional flour as needed to avoid sticking.

Once potato dough has come together, knead until smooth and even, with no visible bits of egg or flour.  Keeping work surface and dough lightly floured, cut dough into 4 even pieces.

With hands, roll each piece into a rope until diameter is about ½ inch thick.

With a knife, cut down the rope to form ½ inch by ½ inch squares.

Dust gnocchi with flour and continue until all dough has been formed into gnocchi.

Discard any irregular shaped gnocchi, as it will not cook evenly.

Place gnocchi on a lightly floured sheet pan until ready to cook and serve.

Bring a large pot of water to a soft boil.  Drop gnocchi into the water, work in batches if necessary, and cook until all gnocchi float to the surface of the water, about 1-2 minutes.

Remove gnocchi from water and place in a large mixing bowl.  Toss with pistachio and basil pesto sauce to taste, season with salt and pepper and serve while hot with freshly grated Parmigiano-Reggiano on the side.
 

Nutritional Facts (Amount per Serving):

Calories 1260, Total Fat 83g, Saturated Fat 14g, Monounsaturated Fat 55g, Cholesterol 200mg, Sodium 3980mg, Potassium 1420mg, Carbohydrate 108g, Dietary Fiber 9g, Protein 25g