Heat half of the oil in a frying pan. Cut the onions into fine strips, add them and fry them at a relatively high temperature until they are brown. Now add the garlic, fry briefly and then pour in the marsala and balsamic vinegar. Bring to a boil, turn down the temperature and let everything simmer gently for 45 minutes without the lid. Then season with salt and freshly ground pepper.
In the meantime, prepare the liver: cut it into strips about 4 cm long and no thicker than thin French fries.
When the 45 minutes are up, heat the remaining oil with the butter in a second frying pan. When the butter is foaming, add the liver cut into strips and fry briefly. It only takes 1-2 minutes to brown and shouldn`t be fried too long, otherwise it will get dry. Immediately pour the finished liver into a preheated bowl, pour the hot onion sauce from the other pan over it and serve immediately.
Potatoes with tomatoes and basil go well with this.