Heat olive oil in a frying pan, add the onions, cook covered for 5-10 minutes over a medium heat, stirring occasionally.
Remove the lid, add balsamic vinegar, season with salt and freshly ground pepper, cook over a high heat for another 5 minutes, stirring often, until caramelized.
In the meantime, place the broccoli in a heatproof bowl, pour over boiling water to cover the broccoli completely. Let it stand for 5 minutes, then drain the water.
Add the broccoli in the pan. Make two wells and crack in the eggs. Cover with a lid and cook over a medium heat for 5-10 minutes, depending on how runny you like your yolk. Enjoy!