Omelette sandwich is literally that: an omelette between two slices of buttered bread.
A one-egg omelette made in a small frying pan (so that you don't have to stir it or disturb it in any way, and it can cook flat). Straight onto the bread while still hot. Slap the second slice of bread on top and trim off the protruding edges of omelette. Allow to cool for a minute or so before wrapping the sandwich up.
I like it plain. Dd likes it best when I spread ketchup on one slice instead of butter.
(BTW I can't email ATM)