Preheat oven at 170C.
In a pan, add carrots, sugar, water and cinnamon stick to make the base for the cake-carrot purée.
Beat walnuts and spices in a mixer. Take out and then in a mixer beat the eggs and brown sugar for 5-6 minutes until fluffy. Add milk, sunflower oil, walnut, vanilla extract in the mixture and beat for about 1 minute. Add flour and 100g of the carrot purée and beat on high speed to avoid for the cake to become bread-y. 
Butter up a round baking dish, add the carrot mixture in and bake for 40 minutes.

For the frosting

Mix well cream cheese and 100g of the carrot purée in a bowl. 
Spread frosting on the cake and garnish with orange zest and walnuts.