Heat some olive oil and butter in a frying pan and gently sauté the onions for 20 minutes or so, until they soften and collapse to a lovely golden-brown heap. Add a little water or stock from time to time to keep them moist. Remove from the pan and set aside.
Heat a little more oil and butter in the pan and quickly sauté the liver until brown on all sides. Season with salt and pepper. The cooking should only take a few minutes.
Add a splash of balsamic vinegar and return the onions to the pan to warm through.
Eat immediately with a little wilted spinach or grilled polenta.