To make the gnocchi: Take the potatoes (unpeeled) and cook them in boiling salted water. Cook the potatoes until they are soft when pierced with a fork. Remove from the water and peel the potatoes as soon as they are cool enough to handle. Puree the potatoes through a food mill and make sure there are no lumps. Once the potatoes have cooled a bit more, add the egg yolks and incorporate. Then add all of the other ingredients and gently work the dough until all components are worked in. Divide the dough into equal parts and start to roll the dough into thin logs. Dust the table with the flour to make rolling easier. Cut into small pieces across the dough with the back of the knife or a bench scraper and store the gnocchi on a pan with more flour on it.
To make the sauce: Melt butter in saucepan. Add vegetables. Saute for 1 minute. Add all remaining ingredients except cheese and chives. Reserve.
To assemble: Bring a large pot of salted water to a boil and add gnocchi. Cook for approximately1 minutes. Drain well and add to finished sauce. Toss gnocchi with sauce, add cheese and chives and serve.
Recipe courtesy of Michael Schlow, Radius