Preheat the oven to 150C/130C Fan/Gas 2. Oil and line a 900g/2lb loaf tin (approximately 13x23cm/5x9in) with baking paper.
For the carrot cake, beat the eggs in a large bowl, then add the oil, brown sugar, grated carrot, raisins and chopped nuts.
Sift in the remaining cake ingredients and mix using a wooden or large metal spoon until well combined.
Pour the mixture into the prepared loaf tin, smooth the surface and bake for 1 hour 15 minutes, or until a skewer inserted into the middle comes out clean.
Remove from the oven and allow the cake to cool in the tin for about 5 minutes before removing. Cool completely on a wire rack before serving.
For the icing, beat the cream cheese and butter together in a bowl until well combined. Add the vanilla extract, icing sugar and orange zest and mix until the icing is smooth and thick. Using a palette knife, spread the icing evenly over the cooled cake, dipping the knife into a bowl of hot water if the icing is hard to spread out. Cut into slices to serve.