When the onion is ready, push it to the edges of the skillet. Add a bit more olive oil if need be, raise the heat, and add sliced calf’s liver, trimmed and sliced into thin strips, to the skillet. Sauté over lively heat, just until the liver has lost its raw color. Then mix the onions and liver well, adding a handful of finely chopped parsley to the mix and seasoning well with salt and pepper. After a minute or so, remove the liver and onions to a warm serving plate.
Add a good slash of white wine to the skillet and deglaze, scraping up the sucs that will have formed with a wooden spoon or spatula. When the wine has reduced to a syrupy consistency, pour it over liver, sprinkle with some additional chopped parsley and serve immediately.
As for measurement, the main point is to use an approximately 1:1 ratio of onion and liver by weight. The flavor of the onion must balance that of the liver, but not to overwhelm it. The rest is entirely a matter of taste.
Some recipes, by the way, call for liver than has been cut into small pieces rather than strips. But I find the strips give the dish a more delicate flavor—the liver melds more completely with the other ingredients—and makes the liver cook more quickly, which keeps it tender. Liver slices bought at the store often need to be well trimmed of any ‘skin’ left around the edges, If you leave the skin on, the liver will tend to curl up, although cutting it into strips will also help avoid this. You can also make lamb’s liver this way, and it will be very good. Beef liver, however, is a bit too strong for this treatment.
The final deglazing of the skillet after having removed the liver and onions is actually my personal take on the dish. The original recipe calls for adding the liquid—be it vinegar, wine, lemon juice, plus, in some recipes, a bit of broth—to the skillet with the liver and onions and allowing the whole to simmer together for a few minutes. But I like my liver still pink inside, so I remove it as soon as it is cooked to my taste.
Some recipes call for you to remove the onions from the skillet before you add the liver, then add it back when the liver is almost done. This avoids any risk of the onion burning, but if you slice the liver into strips, it cooks so quickly there is little risk of that.
The most typical way to serve fegato alla veneziana is with polenta, either warm and soft or cooled, cut into squares and grilled. In the Veneto, by the way, the usual polenta is made with white polenta flour. Served this way, the dish can be a piatto unico. But if you want to precede your liver with a primo, it is perfectly delicious accompanied by some steamed potatoes or simply by itself, along with some crusty bread to sop up those wonderful juices.
The original name of the dish, in Venetian dialect, is figà àea Venessiana. The dish has a longer history, with antecedents going back to ancient Roman days, when they would combine liver with figs, with the same intention of balancing the flavor of the liver with something sweet.