For the pasta dough: Put the flour in a pile on a clean, dry work surface. Make a well, about 8-inches wide, in the center of the flour pile. Crack all the eggs into the hole, add the olive oil and salt, and beat the eggs with a fork. Using the fork, slowly begin to incorporate the flour into the egg mixture. Do not worry about the lumps.
When most of the flour is incorporated begin kneading the dough with your hands. Knead until it is smooth and supple, about 10 to15 minutes. It is really important to put your whole body into kneading otherwise the pasta will not develop the proper consistency. You need to knead! Wrap the dough in plastic wrap and let it relax for at least 1 hour. If using immediately do not refrigerate.
While the dough is resting, make the filling: Combine all of the filling ingredients in a large bowl. Taste to make sure it is delicious. Put it in a pastry bag and refrigerate until ready to use.
Roll the pasta: Set the pasta roller on the widest setting. Start with half the pasta dough. Using your hands flatten the dough as much as you can to facilitate it going through the pasta roller. Run the dough through the roller twice dusting it with flour in between rolls if it feels sticky. Fold it into thirds turn it 90 degrees and run it through the pasta machine 2 to 3 times. Continue to run the pasta through the machine reducing the setting between each run. Stop when you get to the second to last setting. Always hold the pasta on the tops of your hands, palms down! If you hold it with your fingers up you will create stretch marks and those are never good.
To assemble the ravioli: Lay the pasta sheet on a floured work surface. Brush the lower half of the pasta (the part that is closest to you) lightly with water. This is the "glue" that will hold the ravioli together. Use the glue sparingly, if you use too much it will slide and not stick. Pipe 1-inch balls of filling onto the pasta that has been brushed with water, leave about 2-inches between each ball. Fold the top half of the pasta over the pasta balls to meet the bottom edge. Using your 2 index fingers poke around each filling ball to seal the ravioli shut and make sure there are no air bubbles. Cut out each ravioli using a fluted round cutter. Transfer to a sheet tray coated with semolina. Cover and set aside until ready to use.
To make the sauce: Coat a large saute pan with extra-virgin olive oil. Add the pancetta and garlic and saute over medium-high heat. When the garlic is light brown and aromatic remove it from the pan and discard it. When the pancetta is crispy add the mushrooms, season with salt, to taste, and cook until they are soft and wilted. Add the chicken stock, and cook until it has reduced by half. Stir in the butter, shaking the pan frequently, and cook until the sauce thickens and looks velvety. Taste for seasoning and add salt, if needed.
Bring a large pot of well-salted water to a boil over medium heat. Add the ravioli and cook for 3 to 4 minutes. Carefully remove the ravioli from the water and immediately put it in the pan with the sauce. Bring to a boil shaking the pan frequently. Remove from the heat, sprinkle in the Parmesan, and swirl until it has combined with the sauce. Transfer to a serving platter and serve immediately, sprinkled with a little more grated Parmesan and chopped chives. Mangia bene!!
Recipe courtesy of Anne Burrell