Place a medium saucepan on a medium high heat. Add a drizzle of oil, the chopped broccoli and a big splash of water.
Cover and cook for about 10 minutes, stirring every 3-4 minutes and adding more water if it starts to burn.
Meanwhile, bring a small pot of water to the boil for the eggs. Add vinegar then break in your eggs. Reduce the heat to a gentle simmer and allow the eggs to gently bubble for about 3 minutes or until they feel soft and pillowy to your finger. (I set a timer otherwise I forget them!)
When the broccoli is no longer crunchy, season generously with sea salt and pepper.
To serve, divide broccoli between two plates and top with poached eggs and mayo.