Preheat oven to 180C/350F. Grease a 20cm cake tin and line with baking paper.
In a mixing bowl, whisk together the eggs and sugar until thick and creamy. Stir in the vanilla, carrots and oil.
Sift the flour, baking soda, baking powder and mixed spice over the mixture and fold in gently. Stir in the nuts.
Spoon mixture into the prepared cake tin. Bake for 40-45 mins or until a skewer inserted into the centre of the cake comes out clean. Leave the cake to cook in the tin.
For the icing, beat the cream cheese until smooth. Add the butter, vanilla and icing sugar; beat until smooth.
When the cake is cold, turn out and remove the paper. Put on a serving plate and spread the icing over the top. Options are to also sprinkle with more nuts.
Recipe Notes
To make this gluten-free: Substitute the 1 1/2 cups of flour with 1C rice flour, 5 tbs potato starch, 3 tbs tapioca starch and 3/4 tsp xanthan gum.