I've seen and answered a similar question about the development of soups everywhere. Soup is even more ubiquitous because water is the most common ingredient, found all over the globe. I think with similar ingredients human cultures will discover similar uses over time, independent of each other. There are only so many things to do with eggs, so people experimented and found out you could incorporate other ingredients into beaten eggs and the eggs would hold them. The techniques and recipes are different in many ways for sure, but ultimately the answer is eggs are eggs no matter where you are, they have similar consistency and cooking time everywhere in the world.