Make the vinegar reduction: Place all the ingredients into a small saucepan and bring to a boil over high heat. Immediately reduce the heat to medium low and cook the mixture on a simmer and allow the vinegar to reduce and thicken, about 12 minutes. Pour the ingredients through a fine mesh sieve into a heatproof bowl. 

Make the whipped cottage cheese: Place cottage cheese in a food processor and blend until smooth, about 1 minute. Slowly pour in the olive oil while the processor is on and continue blending for 2-4 minutes. The cottage cheese should be fluffy and light. Place the cottage cheese mixture  into a bowl, cover, and set the mixture in the refrigerator. 

Make the pasta dough: Place the eggs, egg yolks and olive oil into the bowl of a stand mixer fitted with the dough hook attachment. Mix on low to combine. Add the “00” flour and salt to the bowl and mix on low until the mixture forms a dough. Increase the speed to medium and continue mixing until a smooth dough is formed, about 8 minutes. Once the dough is formed, wrap tightly in plastic wrap and let the dough rest for a minimum of 1 hour at room temperature (the dough can be made and refrigerated a day in advance).

Shape the pasta: After the dough has rested, unwrap the dough and cut it into two equal pieces. Working with one piece of dough, roll it out with a rolling pin on a lightly floured surface, just thin enough to go through the pasta machine. Run the dough through the pasta machine, starting at the thickest setting and reducing the setting after each pass of dough until the dough is about ⅛ inch thin and nearly translucent. Once your pasta is rolled out to your thickness of liking, cut it into 10-12 inch long sheets. Add the linguine or fettuccine cutter attachment to the pasta machine and pass the dough through, creating strands of linguine or fettuccine pasta. You can also cut the pasta by hand, lightly flour each sheet of pasta, roll it up crosswise and cut ¼ inch pieces of pasta crosswise. Lightly toss the pasta to detach the pieces of dough. 

Bring a large pot of heavily salted water to a boil over high heat. In a large bowl, mix the whipped cottage cheese, peppercorn vinegar and ¼ teaspoon of freshly cracked pepper until combined. Drop the pasta into the boiling water and cook for 1 minute. Reserve ½ cup of the pasta water and then drain the pasta in a colander. Toss the pasta in a large bowl with the cottage cheese/vinegar mixture along with some pasta water to loosen the sauce. 

Serve immediately with fresh chives and parmesan cheese.