Preheat the oven to 160°C (315°F/Gas 2–3). Grease a 23cm (9inch) round cake tin and line the base and side with baking paper.
Sift the flours, cinnamon, ginger, nutmeg and bicarbonate of soda into a large bowl and make a well in the centre.
Whisk together the oil, sugar, eggs and golden syrup until combined. Add this mixture to the well in the flour and gradually stir with a metal spoon until smooth. Stir in the carrot and nuts, then spoon into the tin and smooth the surface. Bake for 1½ hours, or until a skewer inserted into the centre of the cake comes out clean. Leave in the tin for 15–20 minutes, then turn out onto a wire rack to cool completely.
Spread the icing over the cake using a flat-bladed knife and sprinkle with nutmeg.