Preheat oven to 325F. Line an 8x8-in baking pan with parchment paper.
Microwave butter and 1/3 cup chocolate chips, stirring at 30 seconds intervals, until melted. Set aside to cool slightly. Stir together cocoa, flour and salt in a medium bowl.
Whisk eggs with sugar and vanilla extract in a large bowl. Add cooled butter-mixture, then stir until combined. Fold in the flour-mixture until almost combined. Stir in beets and remaining 1/3 cup chocolate chips being careful not to overmix. Scrape batter into prepared pan, then smooth top.
Bake until edges are firm and a toothpick inserted in the centre comes away with a few crumbs clinging to it, 25 to 30 minutes.