For the pasta:

Weigh the flour and mound it on a board or in a bowl. Make a well in the center of the mound. Crack the eggs in a separate bowl and pour them into the well.

Beat the eggs with a fork until smooth. Using the tips of your fingers, mix the eggs with the flour, a little at a time, until everything is combined.

Knead the dough for 5-10 minutes, or until smooth. Form into a ball and cover tightly with plastic wrap and let it rest for 30 minutes before rolling it out.

Dust 3 large baking sheets with flour. Roll the dough out and feed through a pasta machine adjusting the settings until setting #7, or roll the dough by hand with a rolling pin, making the dough as thin and uniform as possible. Cut the sheet into a 6-10 inch long sheet and dust with flour. Let it rest for 5 minutes. Roll the sheet of pasta up like a paper towel roll from the shorter edge. Using a non-serrated knife, cut the roll crosswise into ⅖-inch wide slices. Delicately open up the sliced pasta with your hands, dust with a little flour and make into a loose nest. Transfer to the prepared baking sheets and cover with plastic wrap. Repeat with remaining dough until none is left.

Cook the pasta in a large pot of salted boiling water for about 2 minutes, or until al dente (cooked but still slightly firm in the center). Drain and serve with the sauce.

For the sauce:

Heat the oil in a large saucepan over medium-low heat. Add the onion, celery, and carrot and saute for about 5 minutes, or until soft, stirring often. Add the ground beef and stir well with a wooden spoon, breaking up the ground beef and stirring often until the meat is browned, about 5 minutes. Add the red wine and turn up the heat to burn off the alcohol. Add the tomatoes and water, stir well and season with salt and pepper.

Cover and cook over low heat for about 1 hour, stirring occasionally. Add the chopped parsley and remove the saucepan from the heat.

Serve with the cooked and drained pasta topped with Parmigiano-Reggiano.