With a healthy monitor, a lot of eggs IS NOT A PROBLEM. The question is, IS YOUR MONITOR/s HEALTHY? most captives are not very healthy.
Second, eggs are fine, with one major exception, they do not provide roughage. Which is VERY IMPORTANT FOR VARANIDS. So if you feed some furred and feathered items along with your eggs, good on you. Try offerring well developed eggs.
Cooking eggs! WHY? Who cooks them in nature?
Eggs without roughage makes for one messing stinky cage. Just a side benefit.
Eggs are a very natural and utilized food item for many varanids. Consider, they are seasonal and if needed the individual monitors will consume roughage. Even plants like cats do. Yes, all monitors consume plants, WHEN NEEDED.
Well, all that I have worked with and thats a lot.
Anyway, feed eggs if you want, just keep in mind the above. ROUGHAGE is needed.
My bet is, eggs will make such a mess you will happily stop. hahahahahahahahahaha good luck