You can use a flax egg in many baking recipes to make the recipe egg-free or vegan. To make a flax egg, mix 1 tablespoon of ground flax seed with 3 tablespoons of water. Let it "gel" for 10 minutes, then add it to the cookie dough. In this recipe, using a flax egg works, but the cookies are a bit more soft and fragile than if you used an egg.