An omelet (or omelette) was a dish typically prepared with beaten eggs folded around a filling such as cheese, vegetables or meat.
In 2151 Hoshi Sato proposed that Chef could make an omelet for Malcolm Reed for his birthday, after she'd learned that eggs are one of Reed's favorite food. (ENT: "Silent Enemy")
In 2365, Commander Riker manually prepared 'Owon egg omelets for Doctor Pulaski, Lieutenant Commander Data and Lieutenants Worf and La Forge. Riker claimed that the computer lacked the subtlety needed for great cooking. However, only Worf found the omelets to be edible. (TNG: "Time Squared")
The final product of Riker's preparation resembled scrambled eggs much more than traditional omelet.
Clara Sutter enjoyed purple omelettes (which used grape juice for coloration). (TNG: "Imaginary Friend")
Cheese omelettes were a favorite food of Reginald Barclay (VOY: "Pathfinder")
Neelix made several kinds of omelets, including Jibalian seven-spice omelettes and Talaxian omelettes, while serving as the chef aboard the USS Voyager. (VOY: "Prototype", "Imperfection")