1.Preheat oven to 160°C (140°C fan-forced). Line 18 holes of two 12-hole (2-tablespoons/40ml) muffin tins with paper cases.
2.Beat oil, sugar and egg in large bowl with electric mixer until thick and creamy. Stir in carrot and walnuts, then sifted flour and spice. Divide mixture into paper cases.
3.Bake cakes for about 20 minutes. Stand cakes 5 minutes before turning top-side up onto wire rack to cool.
4.To make frosting, beat cream cheese, butter and rind in small bowl with electric mixer until light and fluffy; gradually beat in sifted icing sugar.
5.Spoon frosting into piping bag fitted with 2cm fluted tube; pipe frosting onto cakes. Sprinkle cakes with combined pepitas, apricots and extra walnuts.