Peel and slice the onions. Melt the duck fat (or goose fat) in a large frying pan (skillet) over a low heat. Add the onions and the salt and cook very slowly for 15-20 minutes, stirring occasionally to prevent them from sticking.
When the onions have softened and are tinged golden brown, add the sugar and balsamic vinegar to start the caramelisation process. Cook over a low heat for a further 5-10 minutes, stirring occasionally, until the onions are sticky and caramelised.