Whisk flour with cocoa powder and salt in a medium bowl.
Microwave chocolate in a small bowl until melted, about 1 min. Or heat over a small pot of simmering water until melted. Stir in canola oil until smooth.
Whisk eggs with granulated sugar and vanilla in a large bowl.
Whisk in chocolate mixture, then fold in flour mixture and 2 cups grated beets until just combined. Scrape into an oiled 8 × 8-in. metal baking pan.
Bake at 325F until a skewer inserted into the centre comes out clean, 45 to 50 min. Cool on a rack before cutting into squares.