To make the pasta, make a mound 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 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 to retain the well shape. Do not worry that this initial phase looks messy. 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 leftover crusty bits. Discard these bits. Lightly flour the board and continue kneading for 3 more minutes. The dough should be elastic and a little sticky. Continue to knead it for another 3 minutes, remembering to dust your board when necessary. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature.
Meanwhile, to make the filling, in a large bowl, combine the ricotta and the pecorino and mix well. Add the parsley, eggs, basil, prosciutto and nutmeg and stir well to combine. Set aside.
Roll out pasta to the thinnest setting on a pasta rolling machine and place on a lightly floured surface.
If you have a ravioli-cutting rolling pin, cover the layer of pasta with a 1/4-inch thick layer of the ricotta mixture. Place an equal sheet of pasta over and press down lightly with your hands. Carefully roll the 2 sheets together with the roller to form the ravioli. Using a pastry cutter, cut the ravioli apart by running down between the ravioli.
If you do not have a ravioli-cutting rolling pin, then cut a single sheet of pasta at a time into rectangles 2 by 1-inch. Place a teaspoon of the ricotta mixture into the center of each rectangle and fold the pasta down like a piece of notebook paper and seal to form a 1-inch square. Repeat until all ingredients have been used.
Bring 8 quarts of water to boil and add 3 tablespoons salt. Drop the ravioli in and cook 6 to 7 minutes, until tender and fully cooked. Meanwhile, in a 12 to 14-inch saute pan, heat the butter until melted and bubbling. Emulsify with 4 tablespoons pasta water taken from the pasta pot. Remove ravioli from cooking liquid, drain and add to saute pan. Toss over heat 1 minute to coat, and serve immediately.