Preheat your oven to 200 degrees Celsius. Spread butter or coconut oil over the walls of a round cake dish with a diameter of 26 centimetres. Grind the walnuts in a blender. Crack the eggs into a mixing bowl. Add the sugar and the vanilla essence and stir it well.
Adjoin the cocoa, the coconut oil and the walnuts and stir. Mix the flour with the baking powder, add it to the mixing bowl and combine well. Fill the dough immediately into the cake dish and put it into the oven. Bake at 200 degrees for around 40 minutes. You can check if your cake is done with the help of a toothpick: Insert it in the middle of the cake. If it comes out clean, your cake is ready.
For the icing mix the icing sugar in a little bowl with just enough water to melt it. Around two tablespoons are enough to get a thick icing sugar solution. Spread this over the cake and let it set.