A cheese omelette was a dish made by heating the emulsified egg contents until coagulated and applying cheese over the hot egg. The dish was typically served as a breakfast course.
Reginald Barclay was known for his cheese omelettes. In 2376, Harry Kim asked a holographically-visiting Barclay to make one of his famous cheese omelettes for Kim and Tom Paris. Barclay declined, as he didn't have the time due to a very important briefing he was to attend.(VOY: "Pathfinder")