Preheat the oven to gas 4, 180°C, fan 160°C. Butter a 23cm (9in) deep springform cake tin and line with nonstick baking paper.
Pour the oil into a large bowl, add the sugars and beat with an electric hand whisk until well mixed. Add the eggs, one by one, beating well after each addition.
Fold in the flour, baking powder, bicarbonate of soda, ground cinnamon and salt. Then carefully fold in the grated carrots, chopped walnuts and sultanas (if using). Pour into the prepared tin and smooth the surface.
Bake on the middle shelf of the oven for 45 minutes. Then turn down the oven to gas 3, 170°C, fan 150°C and bake for a further 20 minutes or until a skewer comes out clean when inserted into the middle of the cake. Leave to cool for 10 minutes in the tin, then turn out onto a wire rack. Leave to cool completely, then cut the cake in two horizontally and set aside.
For the icing, put the cream cheese, butter and vanilla seeds into a food processor and blend until smooth. Then add the icing sugar and blend again until smooth. Put in a bowl and chill for 30 minutes.
To assemble the cake, spread half the icing on one half of the cake. Put the other half back on top and then cover the top of the cake with the rest of the icing. Decorate with the walnut halves.