Preheat the oven to 180°C/gas mark 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 tsp cinnamon and a pinch of salt, then carefully fold in the carrots, walnuts and sultanas. Tip into the prepared tin and smooth the surface.
Bake on the middle shelf of the oven for 45 minutes. Reduce the oven temperature to 160°C/gas mark 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 on to a wire rack to cool completely.
Blend the cream cheese, butter and vanilla seeds with a whisk or food processor 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.