Preheat your oven to 350°F (175°C). Grease the 9-inch round cake pan and line the bottom with parchment paper.
In a mixing bowl, combine the all-purpose flour, cocoa powder, baking powder, baking soda, and salt. Whisk until well combined.
In another mixing bowl, mix the sugar, vegetable oil, eggs, and vanilla extract. Whisk until the mixture is smooth.
Add the cooked and pureed beets and buttermilk to the wet ingredients, mixing until fully incorporated.
Gradually fold the dry ingredients into the wet mixture using a rubber spatula, being careful not to overmix.
Pour the batter into the prepared cake pan and smooth the top with the spatula.
Bake in the preheated oven for 30 minutes or until a toothpick inserted in the center comes out clean. Remove from the oven and let it cool in the pan for 10 minutes before transferring to a wire rack to cool completely.
While the cake is cooling, prepare the beet-vanilla glaze. In a blender or food processor, combine the cooked and pureed beets, powdered sugar, vanilla extract, and milk. Blend until smooth and adjust the consistency by adding more milk if necessary.
Once the cake is completely cooled, pour the beet-vanilla glaze over the top of the cake, allowing it to drip down the sides.
Slice and serve your delicious chocolate beet cake!