Eggs play an important role in baking. They're used in brownies, cakes, cookies and muffins, and perform several important functions in the baking process. While it's possible to bake brownies without eggs successfully, they need to be replaced with something else that can perform the same function. Omit the eggs from the brownie batter without a proper substitute and what you'll have is a sad batch of brownies.
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Imagine the scenario where with chocolate on your mind and very little time, you hurriedly mixed the brownie batter and plopped it in a pan. Ten minutes later when the timer rang, you pulled them out of the oven, your happy anticipation instantly turning to bitter disappointment. And, then it hit you: You forgot the eggs. To understand why these brownies that were supposed to be soft and chewy are instead flat and hard requires a little research into the function of eggs in baking.
Eggs as Emulsifier
Emulsifier is another word for binder and because eggs are both fat (yolks) and protein (whites), mixing them into brownie batter helps them bind the fat ingredients with other ingredients. In other words, eggs bind oil to water, and keep them from separating while they bake. It works because the protein in eggs is composed of both amino acids that attract water and amino acids that repel it. The water-attracting amino acids bind with the water-based liquid ingredients, and the water-repelling amino acids bind with the oils.
Eggs as Leavening Agent
During the process of binding, another important reaction in the making is called leavening. As the eggs are thoroughly mixed into the batter, often 1 at a time, the water-repelling amino acids in the eggs bind with air to create air bubbles. The water-attracting amino acids bind with the rest of the ingredients, creating a structure that holds the air bubbles in place. During baking, heat causes the air bubbles to expand and pop while the batter surrounding the air bubbles remains intact. The trapped, expanding air causes the brownies (or cake or cookies) to rise, creating a structure that is light and fluffy in proportion to the number of eggs used. Brownies tend to be more dense than cake because they use fewer eggs.
Egg Substitutes in Baking
Back to the idea of intentional eggless baking, perhaps you're out of eggs or maybe an egg allergy has you searching for alternatives. The substitute used will depend on the particular function. In making brownies, the eggs function as both an emulsifier and a leavening agent. In this case, the correct egg substitute will probably be a blend of ingredients. Alternative emulsifiers are ground flax, arrowroot powder, soy lecithin, pureed bananas or other fruit, silken tofu or vegetarian gelatin. The best leavening alternatives are baking soda or baking powder. But don't add more of these if the recipe already includes them. Instead opt for a dairy replacement like yogurt or buttermilk, or a commercially made egg replacement.