How to Make It
Make the dough In a food processor, combine all of the ingredients and process until crumbly. Gather the dough and knead until smooth. Wrap tightly in plastic and let stand at room temperature for 30 minutes.
Make the filling Heat the olive oil in a saucepan. Add the onion and cook until softened. Add the parsnips and 1/2 cup of water, cover and simmer until tender, about 15 minutes. Uncover and boil to evaporate any water.
Transfer the vegetables to the food processor and puree. Stir in the Parmigiano and Champagne vinegar and season with salt. Let the filling cool slightly, then scrape it into a pastry bag fitted with a 1/2-inch tip.
Cut the pasta dough into 4 pieces and keep wrapped. Using a hand-cranked pasta machine and dusting lightly with flour, run each piece of dough through each setting 3 times, beginning at the widest setting and ending at the second-to-the-narrowest. Place the pasta sheet on a floured work surface and cover with wax paper. Repeat with the remaining 3 pieces of pasta dough.
Working with one sheet at a time, cut the pasta into 2-inch squares. Lightly moisten the edges with water and pipe a scant teaspoon of parsnip filling in the center of each square. Fold the pasta corner to corner to form triangles and press out any air. Trim the edges with a fluted pastry wheel. Transfer the triangoli to a floured baking sheet.
Bring a large pot of generously salted water to a boil. Add the triangoli all at once and cook until al dente, about 5 minutes. Drain, reserving 1/2 cup of the cooking water.
In a large skillet, melt the butter in the cooking water, swirling the pan until a creamy sauce forms. Add the triangoli and cook over moderately high heat until hot and coated with sauce. Transfer to plates. Garnish the triangoli with chives and parsley, drizzle aged balsamic on top and serve right away.
Doppio zero or “00” flour, a fine Italian flour, is available online at amazon.com.