1. In a skillet, melt 2 tablespoons of butter. Cook the onions for 1 minute.
2. Pour in the balsamic vinegar and reduce for 2 minutes. Remove from heat and set aside.
3. In a large bowl, whisk the eggs into an omelette. When they are well aerated, season with salt and pepper.
4. In a non-stick pan, melt the butter. Pour in the beaten eggs and cook the omelette over medium heat, bringing the eggs from the sides to the center so that the mixture cooks evenly.
5. Transfer the onions to the omelette. Fold the omelette. Cover and let it rest for 2 minutes.