Line a 23cm round cake tin with non-stick baking parchment. Beat the butter until very soft, then add the sugar and keep beating until the mixture is really fluffy. Finely grate the carrots and blot with kitchen roll to mop up any excess moisture. Add them to the butter mixture with all the remaining cake ingredients and beat thoroughly. Add a splash of milk if the mixture is too stiff. Spoon into the lined tin and level the surface. Bake at gas mark 4/180ºC/350ºF for 1 hour and 15 minutes, covering the top of the cake with a piece of kitchen foil after 30 minutes to stop it getting too brown. Set aside to cool. To make the icing, beat the butter until fluffy, then beat in the icing sugar. Mix in the grated lemon rind. Add a splash of milk to soften the consistency slightly. Swirl the icing on top of the cake once it has cooled and sprinkle with walnuts, if you like.