To Make 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 pancotti 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.