Beat the butter and sugar together (by hand or an eclectic mixer) until light and fluffy.
Add the eggs and beat until well combined.
Grate the beetroot with the fine side of the grater (no need to peel.) Add to the mix, along with the cayenne pepper and cinnamon, lightly stirring only until combined.
Fold the flour and baking soda into the mixture until the flower is combined (do not overmix.)
Transfer the dough to a cake tin or small casserole dish and cook in the pre-heated oven for 35 minutes.
Allow the cake to cool for 20 minutes before removing it from the tin.
Making the topping and finishing the cake
Combine the powdered sugar, cocoa, and water (adjust to make a good consistency) and mix until smooth.
Drizzle the topping onto the cake and allow it to set.