For compost, use the egg's as discarded.
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I have heard this is an extremely successful method. Keep me posted on how it works out for you all.
When I lived in Northern Ontario, we had a compost pile, as did many of our neighbors. We tossed cooked veggie left overs in there as well as the raw trimmings, peelings and rotten ones. Cooked or not didn't make any difference in break-down. Cooked has less of the good stuff than raw, but it's still better going back to the soil than in the landfill.