Line a 8x8 inch pan with parchment paper and preheat the oven to 350 degrees F.
Beat aquafaba with cream of tartar for 5 minutes until stiff peaks form. I use my stand mixer with whisk attachment, but you can use an electric hand mixer. Slowly add in the sugar, about 1/4 cup at a time, until it's all incorporated. It should be very fluffy at this point with stiff peaks. Beat in the vanilla and set aside.
In a microwave safe bowl, add the chocolate chips and vegan butter. Melt in the microwave in 30 second intervals, whisking well at each interval, until melted.
Pour the melted chocolate/butter mixture into the aquafaba mixture and stir gently with a spatula. The aquafaba mixture will shrink at this point but that is fine.
To a medium bowl, whisk the flour, cocoa, baking powder and salt together until combined and no clumps remain. If your cocoa is really clumpy, use a sifter.
Add the dry ingredients to the wet and stir until combined using a spatula. Fold in the additional chocolate chips, if using. Pour the brownie batter into the prepared pan, even it out with a spatula or your hands and bake for 35-37 minutes until the top is shiny.
Let cool for at least 30 minutes as the brownies will firm up as they cool. Enjoy!