Panzotti: Rinse and dry zucchini and trim both ends. Slice into 1/16th-inch rounds and set aside. In a 10 to 12-inch saute pan, heat olive oil until smoking. Add onion and garlic and cook over medium heat until lightly browned and softened, about 8 to 10 minutes. Add zucchini and oregano leaves and cook until very soft, about 7 to 8 minutes. Remove from heat and allow to cool.
In a mixing bowl, stir together coated zucchini mixture, egg, ricotta, Pecorino, nutmeg and parsley until well mixed and season lightly with salt and pepper. Roll out pasta into sheets on second thinnest setting and cut into 3-inch rounds with 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 water to boil and add 2 tablespoons salt. Drop panzotti into water and cook until pasta is tender, about 3 to 4 minutes.
Meanwhile, melt butter in a 12 to 14-inch saute pan and add sage leaves. Drain pasta in a colander and pour into butter mixture. Toss to coat well and pour into heated pasta dish. Shave cacio over pasta using a vegetable peeler and serve.
Mound the flour in the center of a large wooden cutting board. Make a well in the center of the flour and add water a little at a time, stirring with your hands until a dough is formed. As you incorporate the water, keep pushing the flour up to retain the well shape (do not worry if it looks messy). The dough will come together in a shaggy mass when about half of the flour is incorporated. You may need more or less water, depending on the humidity in your kitchen.
Start kneading the dough with both hands, primarily using the palms of your hands. Once the dough is a cohesive mass, remove the dough from the board and scrape up any left over dry bits. Lightly flour the board and continue kneading for 3 more minutes. The dough should be elastic and a little sticky. Continue to knead for another 3 minutes, remembering to dust your board with flour when necessary. Wrap the dough in plastic wrap and set aside for 20 minutes at room temperature. Roll and form as desired.