Preheat oven to 180C/350F. Grease a deep 22cm (9 inch) round cake pan; line the base with baking paper.
Beat oil, sugar and eggs in a small bowl with an electric mixer until thick and creamy. Transfer mixture to a large bowl; stir in carrots, nuts, then sifted dry ingredients.
Pour mixture into pan; bake for about 1 1/4 hours. Stand cake in the pan for 5 minutes before turning, top-side up, onto a wire rack to cool.
Meanwhile, beat butter, cream cheese and rind in a small bowl with an electric mixer until light and fluffy. Gradually beat in sifted icing sugar.