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Roll out the pasta dough to the thinnest setting on a pasta rolling machine. From the thin pasta sheet, cut 12 circles with a 6-inch diameter. Set 6 of the circles on a sheet tray dusted with flour, cover with plastic wrap and set aside.
In the center of each of the remaining 6 circles, mound an equal portion of the ricotta mixture. With the back of a small ladle or spoon, hollow out a well in the center of each mound. Carefully break the eggs, 1 at a time, into a small bowl, and transfer 1 yolk and a bit of white into the center of each well. It is imperative that the yolk remain unbroken.
Cover each filled circle of pasta with an unfilled circle, and press the edges together with fingers to seal.
Bring 6 quarts of water to a boil and add 2 tablespoons salt. Gently, using a wide spatula, lower each ravioli into the water to cook for 2 minutes. Remove from the water and place gently into a 12 to14-inch saute pan with the remaining butter, shave the remaining truffle over, add a generous grating of Parmigiano-Reggiano and carefully put 1 on each plate.
As you expand the well, keep pushing the flour up from the base of the mound to retain the well shape. 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 discard any leftover bits. Lightly reflour the board and continue kneading for 6 more minutes. The dough should be elastic and a little sticky. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature. Roll or shape as desired.