This fast and easy substitute is also completely vegan.
Whether you're out of eggs or baking for a vegan or someone with egg allergies, figuring out how to replace eggs in baked goods can be daunting. But one memorable day at my culinary school, Natural Gourmet Institute, the inimitable Chef Elliott guided me and my culinary school comrades through an epic exercise known as the "Converting Practicum." During the flour-dusted, sugar-fueled hours that followed, we broke up into small teams to tackle baking staples like chocolate chip cookies, banana cupcakes, carrot cake, chocolate brownies, peanut butter cookies, oatmeal-raisin cookies, and more.
My partner Chanelle and I proceeded to make carrot cake for oh, the next hundred hours, tweaking and tasting the recipe each time — carrot cake "as is," carrot cake with a butter substitute, carrot cake with an egg substitute, carrot cake with spelt flour...you get the idea. After sampling all 500 of the class's creations (for research's sake, of course), we learned how baking swaps like coconut oil for butter, maple crystals for white sugar, and applesauce for eggs affect the taste and texture of the final products.
My real takeaway from the day though? Man, does flaxseed make a good substitute for eggs. As Epicurious notes, making a flax egg is simple: Combine three tablespoons water with one tablespoon ground golden flaxseed in a small bowl. Stir together and let the mixture rest for five or so minutes. The flax egg will have a goopy texture that's reminiscent of the real deal. If a baked good calls for more than one egg, use a flax egg 1:1 (so two eggs would be the equivalent of six tablespoons water with two tablespoons ground flaxseed). Obviously, for egg-centric recipes like soufflé you're out of luck with this method.
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I've been using flax eggs for years now in items as varied as muffins, cookies, and waffles with one notable exception — I've never made carrot cake again.