Preheat the oven to 180C/350F/Gas 4.
In a bowl, whisk together the oil, eggs and honey until well combined.
Stir in the flour, baking powder, bicarbonate of soda, salt, vanilla essence and grated carrots and beat well.
Pour the cake mixture into a greased 23cm/9in cake tin and transfer to the oven to bake for one hour until a skewer poked into the centre comes out clean. Leave to cool on a wire rack and carefully remove from the tin when cool.
For the icing, beat the cream cheese and butter together in a bowl until light and fluffy. Add the sifted icing sugar and vanilla essence and stir until combined.
Once the cake is cool, using a palate knife, spread the icing across the cake. Serve in slices.