Peel your beets and grate on a small grater until you have about 1.5 cups. Transfer to a colander and press with the back of a large spoon or squeeze with your hands to remove most of the juice from the beets. Save this juice to color your icing!
In a large bowl, whisk together the eggs, sugar and oil until smooth.
Sift the flours into a separate bowl and add the baking powder, sugar and salt. Stir until combined.
Whisk the dry mixture into the wet mixture, then stir in the grated beets. Take a moment to admire the amazingly vibrant pink color beets produce.
Pour the batter into a greased 9-inch baking dish and bake at 350 degrees Fahrenheit for 25-35 minutes, or until a knife or toothpick inserted in the center comes out clean. Let cool while you make your icing.