Make the filling: Bake the potatoes in a preheated 350 degree F. oven until fork tender, about 30 to 40 minutes. Peel, and while still warm, pass through a food mill. In a small saute pan, heat the 2 tablespoons butter over medium heat. Add the shallots and garlic, and cook until soft. In a medium bowl, combine the farmer's cheese, goat cheese, mascarpone, 3 tablespoons Parmesan, the herbs, and the beaten egg. Add the cooked shallots and garlic and the warm potato. Stir until blended (being careful not to overmix, or the mixture will get pasty). Season with salt and pepper. Cover and refrigerate until needed. Then, with lightly moistened hands, roll into 1/2-ounce balls, about the size of golf balls.
Cut the pasta dough into 4 portions and work with 1 portion at a time, keeping the remaining dough covered with plastic wrap. Lightly dust the work surface with flour. With a pasta machine or a rolling pin, roll out the dough about 20 inches long and 4 inches wide. Brush the dough with egg wash and arrange 9 to 10 balls of filling on the lower third of the length of the dough, about 1 to 1 1/2 inches apart.
Fold the top half over to cover the balls. Press the dough around each ball to seal, making sure that you do not have any air pockets. With a 2-inch round cookie cutter, cut the ravioli. Dust a tray with flour and arrange the ravioli on the tray, dusting with more flour. Repeat with the remaining dough, egg wash, and filling. Refrigerate, covered, until needed.
Bring a large pot of salted water to a boil. Cook the ravioli until al dente, about 3 to 4 minutes.
Meanwhile, in a large saute pan, over high heat, add the oil and the remaining butter. Cook the butter until it begins to brown. Drain the ravioli and toss into the browned butter, turning to coat both sides. Add the remaining Parmesan and season with salt and pepper. Garnish with parsley and hazelnuts and serve immediately.
In a food processor fitted with the steel blade, combine the flour, egg yolks, salt, olive oil, and 2 tablespoons of the water. Process until the dough begins to hold together, then stop the machine and pinch the dough to test it. If it's too dry, add up to 1 more tablespoon of water and process until it forms a moist ball. Turn out on a lightly floured smooth work surface and knead by hand, until a smooth ball is formed. Loosely wrap in plastic wrap and let rest at room temperature for 30 minutes to 1 hour.
Cut the dough into 4 equal pieces. Keep the other pieces covered in plastic while you roll out 1 piece at a time, by hand with a rolling pin or through the rollers of a pasta machine, stretching the dough to the desired thickness.
If using a pasta machine, set the rollers at the widest opening. Flatten the first piece of dough into a thick strip no wider than the machine, to enable it to pass through the rollers. If necessary, dust the pasta very lightly with flour. Run the pasta through the machine. Fold in thirds, crosswise, and run through the machine again. Repeat this procedure 2 or more times, until the dough is smooth and somewhat elastic. Set the machine to the next smaller opening and run the dough through the rollers.
Continue rolling and stretching the dough, using the smaller opening each time, until the next to the last or the last opening is reached, dusting lightly with flour only as necessary. (The strip of dough will be long. If you don't have enough space on your worktable, halfway through the rolling process cut the strip of dough in half and continue to work with each piece separately, keeping the unused dough covered).
Adjust the cutting mechanism to the desired width, cut the noodles, and allow them to dry before cooking. A convenient way to dry pasta is to arrange the cut pasta on a pastry tray sprinkled with flour, preferably semolina flour. As 1 layer is completed, sprinkle flour over the noodles, place a piece of parchment paper over them, and continue layering with noodles and flour. Dry for at least 15 to 20 minutes.
Repeat with the remaining pieces of dough.