Over a low heat, fry the onions in the olive oil until they are coloured and very soft - this can take up to 30 minutes. Season with salt and freshly ground pepper, and tip into a bowl.
In a frying pan, heat the butter until foaming. Season the calf's liver with salt and freshly ground pepper, and briefly cook the meat in the butter for about 20 seconds. Transfer to a colander and drain.
Tip the cooked onions back into the liver pan and toss briefly until they are golden brown and slightly scorched.
Return the liver to the pan with the parsley and finally stir in the vinegar. Serve.