Preheat the oven to 160c. Brush a deep, 23cm round cake tin with melted butter or oil. Line the base and sides with baking paper.
Sift together the flours, spices, and soda into a large bowl. Make a well in the centre.
Whisk together the oil, sugar, eggs and syrup in a jug until combined. Gradually stir this mixture into the dry ingredients; stir until smooth.
Stir in the carrot and nuts. Spoon the mixture into the prepared tin; smooth the surface. Bake for 1 hour and 30 minutes or until a skewer comes out clean when inserted in the centre.
Leave the cake in the tin for at least 15 minutes before turning onto a wire rack to cool.
To make the icing: Beat the cream cheese and butter with electric beaters until smooth. Gradually add the icing sugar alternately with the vanilla and juice, beating until light and creamy. Spread the Icing over the cooled cake.
PLEASE NOTE: The cake can be halved horizontally. Sandwich the layers together with half the icing and spread the remainder on top.