Prepare the cake: Preheat the oven to 350°F (176°C) with a rack in the center position. Generously grease a 10-inch (or 12-inch) bundt pan with baking spray and set aside. Drain the beets, reserving 1 to 2 tablespoons of the liquid for preparing the beet glaze. In a small food processor, purée the beets until very smooth. Reserve 1 tablespoon of the beet purée for the glaze, as well, and set aside for later.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. In a stand mixer bowl, fitted with whisk attachment, combine the sugar, oil, and eggs. Beat at medium speed for 1 to 2 minutes or until smooth. Add the beet puree (aside from the reserved tablespoon), cooled melted chocolate, and vanilla extract. Beat at medium speed for 30 seconds or until smooth. Reduce the speed to low and slowly add the flour mixture, allowing it to incorporate fully with each addition. Scrape down the bottom of the bowl to ensure all of the ingredients are incorporated. If you don't have a stand mixer, you can prepare this batter using mixing bowls and a good-quality whisk.
Transfer the batter to the greased bundt pan, smooth, and bake for 45 to 55 minutes, or until a toothpick inserted in the center comes out clean with some moist crumbs. Allow the cake to cool in the pan on a wire rack for 10 to 15 minutes. Carefulyl invert, remove the cake from the pan, and allow the cake to cool completely on a rack before glazing.
Prepare the glaze: In a small bowl, whisk together the powdered sugar, reserved beet puree, and roughly 1 teaspoon of the canned beet juice. If the glaze is too thick, add an additional teaspoon of beet juice at a time until the glaze is thin enough to drizzle from a spoon. Drizzle the cooled cake with the glaze in a zigzag motion (or in one layer). Allow the glaze to set before slicing.
Leftover cake can be wrapped well and stored at room temperature for 3 to 4 days.
Tips for Success:
Organic powdered sugar is not as white as regular powdered sugar and will produce a slightly more muted glaze color.