Preheat oven to 350°F.
Line a 9-inch by 9-inch brownie pan with parchment paper or grease pan.
Quarter beets and transfer to food processor. Process until pureed, scraping the sides down.
Cut butter into tablespoon size chunks and place in a heavy saucepan. Add chopped chocolate and cook over low heat, stirring constantly until mixture melts and is smooth. Remove the pan from heat and set aside to cool.
In a medium bowl, whisk together flour, baking powder and salt. Set aside.
Using a mixer (hand or stand), gently mix the eggs for about 30 seconds.Add vanilla and brown sugar; mix on medium-high until light and airy - about 2 minutes.Reduce speed and add beet puree and then slowly add chocolate mixture; mix just until combined.Add flour mixture and again, mix just until combined. Pour batter into prepared pan and smooth top with a rubber spatula.
Bake 25 to 30 minutes, until a knife inserted into the centre comes out with just a few moist crumbs sticking to it.
Allow brownies to cool for 5 minutes then transfer with parchment to cooling rack.
Cut and serve warm, at room temperature, or straight from the refrigerator.