Preheat the oven to 350F. Grease an 8-inch round baking pan or a rectangular size pan with oil and dust with flour. Keep it aside to be used later.

Take a mixing bowl and crack the eggs into it. Add sugar and give it a whisk until it all combines to a smooth consistency. Add oil and give it another whisk to mix everything.

Take a separate mixing bowl and whisk all the dry ingredients; the flour, cocoa powder, baking powder, baking soda and salt.

Add the dry ingredients to the wet ingredients bowl and whisk. Then, add the grated beetroot, yogurt, lemon juice and hot water. Give it another whisk to mix everything together to a smooth batter.

Pour the batter into the prepared baking pan. Place the pan on the middle rack of the pre-heated oven. Bake it for 35 to 40 minutes. Poke with a toothpick and if it comes out clean, the cake is done. Else, put it back into the oven for a couple of more minutes. Allow the cake to cool for 15 minutes. Then, release the sides with butter knife, invert the cake on a cooling wire and let it cool completely.

When the cake it completely cooled, prepare the frosting for the cake. Add all the ingredients to a clean dry bowl and whisk until it comes together to form a thick spreadable consistency.

You could layer the cake and frosting. Or you could just spread it on top.