It is very difficult to replace eggs in baking.
Just read an article with a genius egg replacement (which can even be used to make meringue!!!!!!!!!!!!).
Please try it and let me know how you like it.
I’m attaching a copy of the text of the article below. I’ve kept all of The Week’s hotlinks for your reference.
You’ve heard of root-to-stalk and nose-to-tail cooking, but here’s a way to limit waste that may not have crossed your mind: Use the water in a can of chickpeas. Why on earth would you want to do this?
Three tablespoons of chickpea water can replace a whole egg. The substitute works best in recipes like cakes and quick breads, but it can work for cookies, too.
Two tablespoons of chickpea water can replace one egg white. Simply beat the brine as you would an egg white, and in a little extra time, you’ll see magical results. While you may be able to whip egg whites into a desired consistency within a few minutes, whipping chickpea water requires a little extra time. Expect to whip it for at least 15 minutes.
In addition to whipping for longer, you also have to be careful with the temperature. Whether you’re making meringue cookies or meringue topping, never heat the brine above 250 degrees and keep a close eye on the oven.
Skeptical? Thanks to vegan baker Goose Wohlt, who some credit with discovering the brine’s meringue-like properties, there’s a growing movement behind what people are calling “aquafaba.” Dan Barber even used the stuff at his food scraps pop-up wast-ED.