Ever since Alan was able to eat solid food, he does not like eating egg yolks. He will eat hard boil egg whites for breakfast for almost everyday. Sometimes more than 2 eggs a day. This is why we choose to buy a good kind of eggs. Wilcox Farms Omega 3 eggs, hens are fed a vegetarian diet, rich in flax seed. They are fairly affordable too. We always bought ours from Costco. I think this is one of the best kind of eggs to give to a kid.
Here is a short video of my baby having a good time peeling the eggs and eating egg white with broccoli.