Pile flour on a clean, dry work surface and make a well in the center. Add beaten eggs to the well. Push flour into the well of beaten eggs and use your fingers to gather mixture into a shaggy mass. Press dough into a ball and press a finger into the center. If dough sticks to your finger, add a bit more flour and knead once or twice to combine. Clear work surface of excess flour.
Knead dough 7 to 10 minutes, or until soft, smooth, and pliable. Wrap in plastic wrap and set aside for 30 minutes to rest.
While dough rests, make the filling. Bring potatoes to a simmer in a small pot of salted water over medium heat. Simmer 10 to 12 minutes, or until tender. While potatoes are simmering, grind hazelnuts to a coarse meal in a food processor and set aside. Drain potatoes and add to a medium bowl. Mash potatoes and stir in ricotta. Add ground hazelnuts, parmesan, butter, and chives. Stir, taste, and season with salt and pepper. Transfer filling to a pastry bag fitted with a wide tip or a plastic bag with one corner snipped off. Set pastry bag aside.
Flour a clean, dry work surface and set up a pasta machine. Divide dough into 2 pieces and cover the second with a clean dishtowel. (If using a rolling pin, divide dough and roll each piece into long rectangle about 1/16-inch thick). Open pasta maker on the widest setting, press dough into a disk, and feed dough through. Fold into thirds and repeat 2 to 3 times. Narrow the opening between the rollers by one notch, and roll dough once more. If dough feels sticky, sprinkle flour on both sides. Continue reducing the settings and rolling the dough until you’ve rolled it through the narrowest setting. (The pasta sheet should be about 1/16-inch thick and slightly translucent.) Lay sheet of dough on the work surface and trim edges with a pasta cutter or sharp knife to form an even rectangle.
Sprinkle a rimmed baking sheet with flour and coarse cornmeal and set aside. Using a pastry brush and warm water, moisten half the dough. Starting at one end of moistened dough and leaving a ½-inch border along the edge, pipe teaspoon-size dollops of filling along the length of the dough, spaced about ½ inch apart. Fold other side of dough over the filling and press down with your fingers to seal along sides and in between the dollops of filling. Use a pasta cutter or sharp knife to slice between the dollops of filling and make the individual agnolotti. Transfer to the prepared baking sheet and repeat rolling and filling with the second piece of dough. Cover and refrigerate agnolotti until ready to cook. You’ll have between 28 and 32 agnolotti.