"What came first...the chicken or the egg"
I must have an egg
When I first began baking, eggs when into everything and I mean EVERYTHING. I thought it was the soul of my food and nothing baked could exist without it. Eggs were the glue holding it all together and if I dared forget to put 1, 2 or even 3 in the mix the end result would be this week's lucky dog treat because our dog eats anything, including our green tomatoes on the vine but that's another story. Even our biscuits started out with eggs and those that bake are probably cringing since eggs have no business in a biscuit - that is a cardinal sin. One day with everyone arguing that this would be the end of my business, I decided to making something vegan. I started with what I thought would be the most forgiving item - the muffin.
Making a Mix
Many times muffins start with egg and sugar or egg and oil. This time I started with oil and sugar but I quickly realized that sugar never breaks down in oil because there is no enough liquid to encourage friction. Adding a very small amount of milk yielded a creamy sugar substance so I pressed on. I added my own muffin mix with vanilla extract, chocolate chips, coffee (which brings out the flavor of the chocolate) and adds color and a little more milk. The mix looked great but when it baked it cracked badly and took me back to those thoughts of dry vegan food. So I researched and researched and discovered there are many, many substitutes for eggs. The tricky part is what purpose does your egg have in the baked good and how many do you need?
How to replace the egg
Binder - if the egg is serving as a binder, in other words, holding things together try a small amount (and I mean small amount) of xanthum gum. Start with 1/4 tsp per 1/2 cup of flour.
Creaminess - if the recipe needs creaminess there is a whole world of options. You can use different yogurts and creamy substitutes such as tofu, ricotta, sour cream, flaxseed and water, applesauce, bananas, pumpkin puree, coconut cream and Ener-G egg replacer mixed with very warm water
Leavening - if the recipe calls for 3+ eggs then they serve as leavening agents. You can add lift with baking powder and baking soda combination (generally 1 tsp:1/4 tsp ratio respectively), club soda, or yeast. Adding a tablespoon apple cider vinegar also reacts with the baking soda to increase volume.
Whatever you choose to use don't be afraid to hold the egg....you might just surprise yourself.