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In a food processor, combine flour, 2 eggs, 1 tablespoon of the squash puree and salt. Cover and process until well mixed. Add 1 to 2 tablespoons water and process to form a dough that is firm but pliant. Remove the dough and shape into a ball then knead it for about 1 minute or until smooth. Wrap dough in plastic wrap and let stand for 30 minutes.
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Divide dough into four equal pieces. On a lightly floured surface, roll each portion into a 12-inch square. (If using a pasta machine, pass each portion through machine according to the manufacturer's directions until dough is 1/16-inch thick.)
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To shape ravioli, in a small bowl, whisk together the egg and 1 tablespoon water.. Cut rolled dough into 2-inch-wide strips. Brush strips lightly with egg mixture. Leaving a 1/2-inch border around the edges, place about 1 teaspoon of filling at 1-inch intervals on one strip of dough. Lay a second strip of dough, brushed side down, over the first. Using your fingers, press the dough around each mound of filling so that the two moistened strips stick together. Use a round cookie cutter or small cup as your guide and cut dough between filling to make individual round ravioli. You can also cut them into squares. Repeat with the remaining dough and filling. Place the ravioli on a lined cookie sheet or plates as you make them.
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To cook ravioli, boil a large pot of salted water. Gently drop about one-fourth of the ravioli, one at a time, into the boiling water and stir to prevent them from sticking to the bottom of the pan. Simmer gently for 3 to 4 minutes or until tender. Using a slotted spoon, transfer ravioli to a serving dish.
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While the ravioli is cooking, heat the olive oil and gently cook the garlic, hazelnuts and sage. Drizzle this mixture over the ravioli either on individual plates or on a large serving platter. Sprinkle if desired with additional Parmesan.