Lucky you!! Mine don't like eggs too much and I have chickens!! Everyone has different thoughts on protein. My avian specialist told me I need to start giving them protein via egg, fish, chicken or lean ground beef without any salt for skin, feathers, nails, and beak. Mine doesn't like eggs too much so I poached some tuna (Whole Foods) a tiny bit, poached it and mushed it with seeds. They loved it. I now will give some type of protein per the vet twice a month. I'll try eggs again, we end up giving it to the dogs but hopefully one day they'll do more than a nibble.
I know a lot of people here share their eggs with their birds. The serving size I was given was 1 teaspoon or less per bird (mine are parrotlets, lovebird and budgies).
I'm pretty positive there is no such animal in the world that is pure vegetarian. Even cows will eat chickens.