Almost impossible to make "vegetarian eggs": Eggs where the chickens only eat vegetables. Chickens really like eating insects, so keeping them vegetarian means keeping them inside in a sterile environment. You also have to keep insect protein out of their feed.
Easier just to give up eggs, but I know vegans who do that tend to suffer some nutritional problems in the long run. Eating a few eggs, a little cheese, etc. is better for you.