Preheat the oven to 350°F (175°C). Grease and lightly flour a 9x14-inch or 10x15-inch baking dish.
Melt the vegan dark chocolate chips and vegan butter (or coconut oil) together in a double boiler or a heatproof bowl set over a pot of simmering water, stirring until smooth. Remove from heat and let cool slightly.
Peel and chop the cooked beets. Place them in a food processor or blender and process until almost pureed with small texture remaining, then set aside.
In a small bowl whisk together the all-purpose flour, baking powder, and salt; set aside.
In a large bowl, whisk the VeganEgg powder with the 2 cups ice cold water until smooth and lump-free. Beat in both the brown sugar and white sugar, then add the vanilla extract.
Stir the slightly cooled melted chocolate and butter mixture into the beet purée until well combined, then add this mixture to the bowl with the VeganEgg and sugars and whisk until creamy.
Gradually fold the flour mixture into the wet ingredients with a spatula until just combined and no large streaks of flour remain.
Pour the batter into the prepared baking dish and smooth the top. Bake in the preheated oven for 55 minutes.
Remove from the oven; a toothpick inserted may come out slightly wet. Allow the brownies to cool at least 30 minutes, and they are best when cooled completely before cutting.