Cut the white ends off the asparagus. In this case because they were a bit too long I cut the ends in little pieces so that they cook faster

Add the asparagus ends in a pan with melted butter (golden not brown). These need to cook longer than the tips so cook these for around 5 min on their own

Add the tips and some water and close with a lid so that they get steamed. Keep adding water a little at the time as needed so that they don’t burn

When cooked (you can test this by testing it with a fork) add a generous handful of Parmesan and crack both eggs on top. Cover with a lid again so that the eggs cooks with steam without any need for oil or flipping