Can you boil vegetables along with eggs?

Yes, you can do this. Be aware that:

• if you add lots of cool items to boiling water it will take longer to start boiling again, which may impact cooking time a little.
• I can imagine vegetables with very strong colour (beetroot) or flavour (garlic?) might diffuse through the eggshell and give you a pink or slightly garlicky egg.

As most ways** of cooking eggs call for cooking by time, I wouldn't recommend it.

There's nothing, however, to stop you from fishing out the eggs after they're done, and then warming the water back up to cook your vegetables.

This is easier than than trying to remove one item while leaving the other to continue cooking, or experimenting with correct timing on when to add the second item to have two items done at the same time. (which I do with brocolli florets and pasta, adding the brocolli about 2-3 minutes before the time mentioned on the pasta box ... but I'm also eating the two together, so there's no need to separate them)

**There are some devices that you can keep with your eggs, and then add to the water and they'll beep to alert when they're at various temperatures that correspond to soft boiled, hard boiled, or dipping eggs. I've never used them, but I have one that I was given as a gift last year. You still run into the other problems, however.

My mother used to put the eggs in a plastic bag in with the potatoes.

If you want hard boiled eggs, as she did, you can put them in with the cold patatoes and cold water. Take them out 10 minutes after the pot comes to the boil.

The plastic bag in case the eggs cracked. And because our eggs can be dirty, it also keeps the eggs from getting the veggies on them.

It's pretty safe.

Just boil each element the amount of time it requires, and if the eggs go in after the vegetables are already in, make sure that the eggs are at least room-temperature in order to prevent the water from stop boiling.

It's actually a thing to hard boil eggs in a hot pot, which as you know, is usually enjoyed with a variety of different vegetables.