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Heat oven to 180C/160C fan/gas 4. Grease and line a 900g/2lb loaf tin with baking parchment.
Beat the butter and sugar until soft and creamy, then stir in the grated carrot and sultanas. Pour the eggs into the mix a little at a time.
Add the flour, cinnamon, baking powder and most of the chopped nuts and mix well. Tip the mix into the loaf tin, then bake for 50-55 mins or until a skewer poked in the middle comes out clean. Allow to cool in the tin for 15 mins, then remove from the tin and cool completely on a wire rack.
Meanwhile, make the icing. Beat the butter in a large bowl until it is really soft, add the icing sugar and cinnamon, then beat until thick and creamy. When the cake is cool, spread the icing on top, then sprinkle with a little more cinnamon and the remaining chopped nuts.