What is the term for 'sunny side up' omelette? I have a technique when cooking omlettes where you only cook them on one side, and gather up the edges - but let the cheese accumulate in the soft centre. 

Friends have suggested several names for this:


scramelette
sunny side up omelette
soft-centred omelette


The thought occurs that there must be a canonical name - which I'd like to know so I can order it at a restaurant. 

My question is: What is the term for 'sunny side up' omelette?
I believe that is called a classic french omelette.
"Sunnyside" comes from frying unbroken eggs, where the yolk resembles the sun, and by not flipping the egg over makes it "Sunnyside up".