Preheat oven to 350 degrees. Line an 8 or 9 inch square baking dish with parchment paper, or grease well with vegan butter.
Whisk together the vegan egg, warm water and the egg substitute product. I used Follow Your Heart's Vegan Egg this time around, but another egg replacer like a flax egg or even silken tofu can work as well. Just be sure to use about ¾ - 1 cup egg replacer liquid total, about two eggs-worth.
Pour the vegan egg mixture into a large mixing bowl. Add in the other wet ingredients: vegan butter, avocado, sugar and vanilla. Beat until smooth, using a hand or stand mixer.
Add the dry ingredients: cocoa powder, baking powder, salt and flour. A gluten-containing flour will allow for the fluffiest brownies, but you could also use a gluten-free flour if needed. Beat until smooth.
Fold in the walnuts. And optional chocolate chunks.
Pour the brownie mixture into the baking dish. Smooth out.
Bake at 350 for about 22-25 minutes, or until the edges begin to pull away from the dish and darken, and the middle of the brownies feel firm to touch, and sturdy when gently pressing down with your hand. Note: For chewier brownies, bake for an additional 3-5 minutes.
Sprinkle with optional fleur de sel. Allow to cool at least twenty minutes before removing the parchment paper and slicing and serving.