In a 12 to 14-inch saucepan, heat the olive oil and butter over a medium-high flame until very hot but not smoking. Add the onion then turn the heat to medium. Sweat over medium heat until softened somewhat, about 5 minutes. Lower the heat and season the onions with a generous sprinkling of salt. Continue cooking, stirring often until well caramelized and jammy. About 30 minutes.

Raise the heat to back up to medium-high and add the chicken livers to the same pan and continue cooking until the livers are slightly browned on all sides, about 7 minutes more.

Add the vinegar and continue cooking until it is completely absorbed and evaporated. Lower the heat to a simmer and continue cooking for 10 minutes more, adding a bit of water if the pan gets too dry.

Bring 6 quarts water to a rolling boil and add 2 tablespoons salt. Add the fettuccine to the boiling water and cook until al dente, about 10-12 minutes. Drain the pasta, reserving 1/2 cup of the cooking water.

Bring the pan with the chicken livers back up to medium-high heat. Add the cooked fettuccine to the pan. Add parsley and toss to combine. Season with salt and pepper. Turn the pasta out onto a large serving platter and top with generous amount of truffle shavings, grated Parmigiano, and a few pinches of pink peppercorns.