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Preheat the oven to 350°F.
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In a bowl, whisk together the oil, eggs and honey until well combined.
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Stir in the flour, baking powder, bicarbonate of soda, salt, vanilla essence and grated carrots and beat well.
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Pour the cake mixture into a greased 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.
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For the frosting, 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.
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Once the cake is cool, using a palate knife, spread the icing across the cake. Serve in slices.