Preheat the oven to 325F.
Whisk the flour with the cocoa powder and salt in a medium bowl.
Melt the chocolate over low heat in a small, heavy-bottomed pot until melted, stirring consistently. Stir the sunflower or canola oil into the melted chocolate until smooth.
Whisk eggs with granulated sugar and vanilla in a large bowl.
Whisk in the chocolate mixture, then fold in the flour mixture and the 2 cups grated beets until just combined.
Scrape into an oiled 8 × 8 inch. metal baking pan. Bake at 325F until a toothpick inserted into the center comes out clean, 45 to 50 min.
Cool on a rack before cutting into squares.