We know it sounds rather strange but it's entirely possible to make a poached style egg using olive oil. No, it's not fried, the main reason is because poaching is conducted at a much lower temperature than frying.
The temp when poaching an egg in oil is kept at a medium heat with lots of oil - because of lots of oil and because it's kept at a low temperature the egg only fries a little on the outside with a soft poached centre.
The recipe we found comes from the Ohjoy blog and offers up some simple to follow steps to have a go yourself at home.
The recipe also includes a great bonus hit for tasty pizza base to place your poached in oil egg on top.