When it’s hot and shimmering, add the onions and cook, stirring frequently with a wooden spoon, until softened and translucent, about 3 minutes. Add the prosciutto and chicken livers and cook, stirring frequently, until the livers are just cooked and still a little pink, about 1 minute. Add the beef, season with salt and black pepper, and cook, breaking up the meat with the back of the spoon, until just cooked and still a little pink, about 5 minutes.