1.Preheat oven to 180°C (160°C fan forced). Line 18 holes of two 12-hole (⅓-cup/80ml) muffin pans with paper cases.
2.Beat oil, sugar and eggs in small bowl with electric mixer until thick. Transfer mixture to large bowl, stir in carrot, nuts, then sifted dry ingredients.
3.Drop ¼ cups of mixture into paper cases. Bake about 30 minutes. Stand cakes in pans 5 minutes before turning, top-side up, onto wire racks to cool.
4.Brush cold cakes with a little jam.
5.Tint ready-made icing pale yellow. Roll icing between sheets of baking (parchment) paper until 5mm (¼ inch) thick. Using cutter, cut 18 x 8cm rounds from the icing; position rounds on cakes. Use the blunt edge of 6cm round cutter to mark the edge of the buttons. Position mini mints to make button holes.