What sort of response were they looking for with that? "How would you like it - boiled, poached, fried, scrambled or turned into an omelette? Or a meringue maybe?"
GP said a restaurant, not a road-side 'caf'/'diner'. They'd be looking to be given something good, whatever the candidate wants/comes up with/thinks they can do well. e.g. a bad candidate returns literally just a fried egg on a plate, a good candidate returns a devilled egg neatly presented, say.
The restaurant owner is interviewing a chef, not a cook. Part of the chef's job will be to innovate -- new dishes for the menu, small changes to existing dishes when customers ask for it or particular ingredients aren't available, something completely different when a coeliac vegan turns up.
It's weird how different industries work - even if they're both creative ones. If a customer under-specifies what they want, and I just make what I think will wow them rather than what they were thinking of but didn't think to tell me, that's a bad job on my part for not engaging with them and finding out what they actually desired.
Not a customer though, an interviewer who asks you how you'd go about designing the architecture for an IoT-controlled fleet of egg-cracking robots.
You might talk in great detail about SoA design, and the interviewer might be hiring for a monolith, but still respect the acumen, you could still be a great fit.
It doesn't mean the chef's only going to be cooking tasting menus any more than it means the engineer has carte blanche over greenfield design or to rewrite an existing project.
off-topic, but since we're talking about chefs, please take a second to remember Frederic Forrest, who died yesterday. Among numerous roles, he played 'Chef' in Apocalypse Now, an amazing, iconic, memorable performance. "Never get out of the boat."
Eggs are versatile and require special handling, so egg dishes are good for showing both creativity and technique. There's a lot to pay attention to: cracking eggs, picking cooking vessels and utensils, seasoning, plating, texture, how fast you move, etc.
Efficiently making an egg dish that can be served to customers would be a pass. The standards depend on the restaurant and the chef that does the interview.
Eggs are also extremely easy to overcook (I'm far from a professional, I think around ~70C/160F, and the temperature tolerance band is quite small), so there's a lot of techniques in controlling the temperature.
My imagined reply - as I am not a chef: "What do you think I am? A hen? If you want an egg dish, ask for it. An extra word won't hurt you. I can't work with tight people, I'm outta here."
https://www.seriouseats.com/classic-french-omelette-recipe