How to Make It
In a large saucepan, heat 2 tablespoons of the olive oil. Season the livers with salt and black pepper. Add half of the livers to the skillet at a time and cook over moderately high heat, stirring occasionally, until deep golden, 3 to 4 minutes; transfer to a plate with a slotted spoon. Let the livers cool, then finely chop.
Add 2 tablespoons of the olive oil to the saucepan along with the celery, onion, carrot, prosciutto, sage and crushed red pepper and cook over moderate heat, scraping up the browned bits from the bottom of the pan, until the vegetables are deep golden, about 10 minutes. Stir in the tomatoes and bay leaf and cook until the liquid is evaporated and the tomatoes start to caramelize, about 20 minutes. Add the wine and cook until almost evaporated, about 3 minutes. Add the stock and simmer until reduced by half, about 20 minutes. Stir in the livers and vinegar and season with salt and black pepper. Discard the bay leaf.
Cook the pasta in a pot of salted boiling water until alÂ dente. Drain, reserving 1 cup of the pasta water. Return the pasta and water to the pot. Add the sugo and the remaining 2 tablespoons of olive oil and toss over moderate heat until a sauce forms, about 2 minutes. Transfer the pasta to a bowl, top with cheese and serve.