Preheat the oven to 200 C / Gas 6. Grease a 23cm cake tin and line with baking parchment.
For the cake:
Sift the flour into a large bowl. Add the sugar, lemon zest, baking powder, all the spices, cocoa powder, salt and pepper.
Beat the eggs and egg yolk lightly and add to the dry ingredients. Mix well till all the dry mixture is incorporated with the egg. Add the oil and mix well till the mixture has a smooth runny consistency.
Peel and grate your apples and carrots. Toast the walnuts in a dry frying pan over a medium heat until fragrant then remove from the pan and chop finely. Add the ingredients to the cake mixture and mix well. Transfer the mixture to the prepared cake tin.
Bake in the preheated over for 35 to 45 minutes or until the cake is risen and firm and a skewer inserted into the centre comes out clean. Remove from the oven and transfer to a cooling rack to cool completely before decorating.
For the frosting:
To make the cream frosting, add the mascarpone and cream cheese to a large bowl. Add vanilla extract, butter and sugar. Mix well with a hand mixer and if you wish to, cover in cling film and add to the fridge for a couple of hours, I find it's easier to pipe that way. If you prefer not to, use it straight out the mixer. I added some pink colouring in mine.
To decorate, place the cake on a serving plate and pipe the icing as desired. Slice and serve.