Preheat the oven to Gas 4, 180°C, fan 160°C. Grease and line the base of a 20cm (8in) round cake tins. Mix the carrots and oil together in a bowl and set aside.
In a separate bowl sift together the flour, bicarbonate of soda, baking powder and ground cinnamon. Set aside.
Using an electric mixer beat the eggs until frothy. Gradually whisk in the sugar and beat for 3-4 minutes until the batter is thick and creamy. Add the vanilla extract and the flour mixture and beat until just incorporated. Fold in the carrot and oil mixture and walnuts using a rubber spatula or large spoon. Place the batter into the cake tin and bake on the centre oven shelf for 60-75 minutes or until a toothpick inserted in the centre comes out clean. After around 45 minutes you may wish to place a sheet on tin foil over the cake to prevent it from browning on top too much.
Remove from oven and let cool on a wire rack for 10 minutes. Turn the cake onto the wire rack, remove the tin and lining paper. Cool completely before icing.
To make the icing, beat the cream cheese and butter with an electric mixer until smooth. Gradually add the icing sugar, mixing on low speed. Beat in the vanilla extract and lemon zest.
Spread the top of the cake with the icing. Cover and refrigerate any leftovers.
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