Trim long roots and greens from beets and clean off any dirt. Dice them into quarters (or smaller, depending on the size of your beets) and set in a pot of water to boil. Boil until easily pierced by a fork, approximately 30 minutes. Drain and let cool until they are comfortably handled.
Preheat oven to 350°F and grease a 9x13 baking pan or line with parchment paper and spray paper
Melt chocolate, butter, and sugar together in a saucepan set over medium-low heat. Whisk until smooth and completely melted. Remove from heat.
Once the beets have cooled, the peels should slip off easily. Place peeled beets in blender or food processor and puree until smooth.
Mix beets, eggs, vanilla, and cocoa powder into melted mixture until well combined.
In a medium bowl, mix together flour, baking powder, and salt. Add the flour mixture to the large bowl and stir until all the flour is incorporated.
Pour into prepared pan and smooth the top.
Bake for 30 minutes, or until a toothpick inserted into the center comes out clean. Let cool as much as possible before cutting. Great the first day, better the second.
For thicker brownies, use a square pan and increase baking time to 40-45 minutes.