Lay out all the ingredients in front of you. It's best to use chilled liver rather than frozen, as the former will be too watery and turn soggy. If you don't like chicken liver, you can safely use beef liver; just remove the membranes, soak it in milk, and cook it a little longer.
If you've chosen frozen liver, defrost it in the refrigerator beforehand. Rinse the liver and pat dry with a paper towel. Cut the meat into 2-3 pieces.
Peel the onion and cut it in half lengthwise with a knife. Cut each half into half rings.
Core the apples and cut them into small slices.
Place the flour in a small but deep bowl. Meanwhile, heat a little oil in a frying pan.
Dredge each liver slice in flour, then place in the pan and fry on both sides. Fry until golden brown (about 7 minutes). No need to add salt! The key is to place the liver in a single layer (so if you have a lot of meat, fry it in batches). If you layer it too many times, the liver will stew rather than fry, which will prevent it from being cooked through. Remove the fried liver from the pan.
Preheat the oven to 180 degrees Celsius (350 degrees Fahrenheit). Meanwhile, reheat the frying pan, but this time for the onions. Fry the onions in a small amount of oil until golden brown.
Pour vinegar into the sautéed mixture, then add granulated sugar. Mix everything thoroughly. Continue frying for 5 minutes, and a couple of minutes before the end, add the apples to the onions and mix again.
Place the fried liver in a baking dish, season with salt and pepper. Top with caramelized onions and apples.
If you're using chicken livers, bake them in the oven for 15 minutes. Use a non-convection setting.
Serve the finished dish with any side dish you like.