Rinse and dry the zucchini and trim both ends. Slice into 1/16-inch rounds and set aside.
In a 12 to 14-inch saute pan, heat the olive oil until smoking. Add the onion and garlic and cook over medium heat until softened and lightly browned, about 8 to 10 minutes. Add the zucchini and oregano leaves and cook until very soft, about 3 to 4 minutes. Remove from heat and allow to cool.
In a mixing bowl, stir together the cooked zucchini mixture, the egg, ricotta, pecorino, nutmeg and parsley until well mixed and season lightly with salt and pepper. Roll out pasta into sheets on the second thinnest setting and cut into 3-inch rounds with a water glass or pasta cutter. Place 1/2-tablespoon zucchini mixture into each and fold into a half moon. Continue until all the pasta is used.
Bring 6 quarts of water to a boil and add 2 tablespoons salt. Drop the panzotti into the water and cook until the pasta is tender, about 3 to 4 minutes.
Meanwhile, melt the butter in a 12 to 14-inch saute pan and add the sage leaves. Drain the pasta in a colander and pour into the butter mixture. Toss to coat well and pour into a heated pasta dish. Shave cacio over the pasta, using a vegetable peeler, and serve.
Mound 3 1/2 cups of the flour in the center of a large wooden cutting board. Make a well in the middle of the flour and add the eggs and the olive oil. Using a fork, beat together the eggs and oil and begin to incorporate the flour, starting with the inner rim of the well.
As you expand the well, keep pushing the flour up from the base of the mound to retain the well shape. The dough will come together when half of the flour is incorporated.
Start kneading the dough with both hands, using the palms of your hands. Once you have a cohesive mass, remove the dough from the board and scrape up and discard any leftover bits. Lightly reflour the board and continue kneading for 6 more minutes. The dough should be elastic and a little sticky. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature. Roll or shape as desired.
Recipe copyright 2000, Mario Batali. All Rights Reserved.