No eggs are necessary in this recipe. The applesauce in the recipe acts as a replacement for eggs, providing moisture and helping to bind the ingredients together. It's a common substitute in vegan and allergy-friendly baking.   If you're not a fan of applesauce, you could also use mashed bananas, yogurt (dairy-free to keep it dairy-free), or a flax egg (1 tablespoon ground flaxseed mixed with 2.5 tablespoons water, left to sit for 5 minutes until it thickens) as an egg substitute.   Please note that the texture might slightly vary depending on the substitute you choose, but overall, it should still yield a tasty batch of brownies.