You need to replace the egg to make a vegan brownie recipe.  There are a couple different substitutes you can use. I prefer to use soft silken tofu for the added moisture it brings.  Simply replace each egg with ¼ cup silken tofu.  I highly recommend squeezing the tofu first just a bit and pureeing it in the blender with the other wet ingredients and then add that to the dry ingredients.  Blending the tofu creates a smooth mixture but also adds some air to the tofu which will give the brownies a bit more lift. Another easy egg substitute for making brownies is to use a chia or flax egg.  Soak 1 tablespoon of ground chia or flax for five minutes in ¼ cup water for each egg in the recipe.  Continue preparing the recipe following the instructions with the egg substitute.