1.Place whole unpeeled mandarins in medium saucepan, cover with cold water; bring to the boil. Drain then repeat process twice. Cool mandarins to room temperature.
2.Preheat oven to 180°C (160°C fan-forced). Line two 12-hole standard (⅓-cup/80ml) muffin pans with paper cases.
3.Use butter that has been stored at room temperature.
4.Blend or process nuts until finely chopped; place in small bowl. Halve mandarins; discard seeds. Blend or process mandarins until pulpy.
5.Beat butter and sugar in small bowl with electric mixer until light and fluffy. Beat in eggs, one at a time. Transfer mixture to large bowl; stir in polenta, baking powder, nuts and mandarin pulp. Divide mixture between paper cases.
6.Bake cakes about 25 minutes. Stand 5 minutes before turning, top-side up, onto wire rack to cool.
7.To make mandarin icing; sift icing sugar into small bowl, stir in butter and enough juice to make icing spreadable.
8.Spread cold cakes with mandarin icing.