Homemade Cheese Ravioli with Sage Butter

Method

1. Make the dough: mound the flour on a clean work surface and make a well in the center. Add the 3 eggs, egg yolk, olive oil, and a pinch of salt to the well.
2. Using a fork, gently beat the eggs, gradually incorporating flour from the inner walls of the well until a shaggy dough forms.
3. Knead the dough by hand for 8 to 10 minutes, dusting with flour as needed, until smooth, elastic, and no longer sticky. Wrap tightly in plastic and let rest at room temperature for 30 minutes.
4. Meanwhile, make the filling: in a medium bowl, stir together the ricotta, Parmesan, 1 egg, nutmeg, 1/2 teaspoon salt, and the pepper until smooth. Refrigerate until ready to use.
5. Divide the rested dough into 4 pieces (keep unused pieces covered). Working with one piece at a time, roll it through a pasta machine, starting at the widest setting and working down to the second-thinnest setting, until you have a long, thin sheet (about 1/16 inch) you can almost see your hand through.
6. Lay the pasta sheet on a lightly floured surface. Place teaspoon-sized mounds of filling about 2 inches apart in a row down one half of the sheet.
7. Lightly brush the dough around each mound with water, then fold the other half of the sheet over the filling, pressing firmly around each mound to seal and push out any air pockets (trapped air can cause ravioli to burst while cooking).
8. Cut the ravioli apart with a knife or fluted pastry wheel into roughly 2-inch squares, pressing the edges once more to ensure a tight seal, then transfer the finished ravioli to a lightly floured baking sheet in a single layer; repeat with the remaining dough and filling.
9. Bring a large pot (6 to 8 quarts) of water to a boil and salt it generously.
10. Carefully drop the ravioli into the boiling water in 2 batches and cook for 3 to 4 minutes, until they float to the surface and the pasta is tender; do not overcrowd or stir too vigorously, or they may split open.
11. While the ravioli cook, melt the butter in a large skillet over medium heat. Cook for 3 to 4 minutes, swirling occasionally, until the butter foams, then turns golden brown and smells nutty.
12. Add the sage leaves to the brown butter and cook for 30 to 45 seconds until crisp; immediately remove the skillet from the heat to stop the butter from burning.
13. Using a slotted spoon, transfer the cooked ravioli directly into the skillet with the sage butter, along with a splash of pasta water, and gently toss to coat.
14. Divide among 4 plates, spoon extra sage butter over the top, and finish with grated Parmesan.