This word is acceptable for play in the US & UK dictionaries that are being used in the following games:

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n. A dish made with beaten eggs cooked in a frying pan without stirring, flipped over to cook on both sides, and sometimes filled or topped with cheese, chives or other foodstuffs

n. beaten eggs or an egg mixture cooked until just set; may be folded around e.g. ham or cheese or jelly

"The BF gets the same, but his omelette is rolled up instead of wrapped around the rice."

dish   

firm omelet    egg fu yung    egg foo yong    fluffy omelet   

you can't make an omelette without breaking eggs   

omelet    omelets    cutlet    cornbread    muffin    croissant    pastry    fritter    sausage    chowder