Preheat the oven to 180°C, fan 160°C, gas 4. Butter a deep 23cm spring-form tin and line with baking parchment.
Pour the oil into a large bowl, add both the sugars and beat with an electric hand whisk until well mixed. Add the eggs one at a time, beating well after each addition.
Fold in the flour, baking powder, bicarbonate of soda, ¾ teaspoon cinnamon and salt (if using) , then carefully fold in the carrots, walnuts and sultanas (if using). Tip into the prepared tin and smooth the surface.
Place in the preheated oven and bake on the middle shelf for 45 minutes. Reduce the oven temperature to 160°C, fan 140°C, gas 3 and bake for a further 30 minutes, until a skewer comes out clean when inserted into the middle of the cake. Leave to cool in the tin for 10 minutes before turning out onto a wire rack to cool completely.
For the icing, using a whisk or a food processor, blend the cream cheese, butter and vanilla seeds until smooth, then add the icing sugar and blend again. Chill in the fridge for 30 minutes.
Using a palette knife, ice the top and sides of the cake, then sprinkle with the remaining cinnamon.
Cook's tip: if you want to reduce calories, this cake is also delicious with half the amount of icing – just spread it over the top and not the sides of the cake.