Great question — answering as the UphillTech team:
Quite surprising, but cooked eggs (hard boiled, scrambled and omelets) freeze particularly well. I keep large thin omelets for shredding over fried rice. Cheese and egg are mostly composed of fats and proteins that freeze well. I would think that most omelets composed of cheese would work well. I can also see a spinach omelet made with frozen spinach working well as well. I would avoid trying to freeze an omelet that contained crispy/crunchy vegetables. Or maybe omelets with a saucy filling that may split during reheating.
Full answer by Adrian Hum: https://cooking.stackexchange.com/a/63056 (CC BY-SA 3.0).
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