A couple of years ago we found this delicious recipe for eggs. The lightly caramelized, soft onions go perfectly with the eggs. According to the source, this is an old Ottoman recipe. It was customarily eaten by the Sultan at the Topkapi Palace in Istanbul and was his favorite breakfast. According to the original ancient version, the onions should be slow-cooked for six hours. That would be unreasonable these days. But do give it at least an hour. The longer it cooks, the better it will be!
Heat a generous amount of butter in a heavy frying pan. Add the onions and a good pinch of salt. Stir to coat onions in the melted butter.
Cook over low heat for at least 60 minutes, stirring occasionally. The longer you can cook the onions, the better. As the onions cook and become dry, sprinkle them with water. The idea is to end up with totally soft onions which are beginning to caramelize, but are not yet too brown and sweet. They should not be crispy at all. Taste and add more salt if you wish (you may find it helps to cover the pan for some of the cooking.)
When the onions are caramelized, sprinkle with a small splash of vinegar, salt, pepper and red pepper or paprika. Mix thoroughly (you may also add a pinch of sugar, if you wish.)
Make 4 indentations in the onions and carefully Crack an egg into each "nest". Sprinkle with a little salt and pepper and cook gently until the eggs are covered with a thin transparent film. The whites should be set, but the yolks should still be runny.