Prepare the Pasta Dough
On a clean surface or in a large mixing bowl, mound the flour and create a well in the center.
Crack the eggs into the well, add a pinch of salt, and, if using, a tablespoon of olive oil.
Gradually mix the eggs with the flour using a fork, pulling in flour from the sides.
Once combined, knead the dough by hand for about 8-10 minutes until it’s smooth and elastic.
Wrap the dough in plastic wrap and let it rest at room temperature for 30 minutes.
Make the Ricotta Filling
In a medium bowl, combine the ricotta, Parmesan, lemon zest, egg yolk, nutmeg, salt, and pepper.
Mix well until smooth. Adjust seasoning to your taste.
From my own personal experience, if the ricotta seems too wet, you can drain it in cheesecloth for about 15-20 minutes before using.
Roll Out the Pasta
After the dough has rested, divide it into smaller portions.
Roll each portion out with a pasta machine or by hand until thin, around 1/16 inch (thinner than a lasagna sheet but thicker than paper).
Cut the dough into 3-4 inch squares using a pastry cutter.
Assemble the Cappellacci
Place a teaspoon of the ricotta filling in the center of each square.
Fold the dough over the filling diagonally to create a triangle. Seal the edges by pressing down with your fingers or a fork.
Then, take the two corners of the triangle and bring them together, pressing firmly to create the signature "hat" shape.
Place the assembled cappellacci on a lightly floured surface to prevent sticking.
Cook the Cappellacci
Bring a large pot of salted water to a boil.
Carefully drop the cappellacci into the water and cook for 5-7 minutes, or until they float to the top.
Using a slotted spoon, remove the cappellacci and drain well.
Prepare the Sauce
In a pan, melt the butter over medium heat until it begins to brown slightly.
Add the sage leaves and let them crisp up in the butter.
Toss the cooked cappellacci in the butter and sage sauce, ensuring each piece is coated.