Preheat oven to 170c. Line a standard 12 muffin tray with patty pans.
Place the brown sugar, oil, golden syrup, eggs and vanilla in a bowl and whisk to combine. Sift the flours, bicarbonate of soda and cinnamon over top and fold through. Add carrot and stir to combine.
Pour mixture into the muffin tray and bake for 20 minutes or until cooked.
To make the icing, place all the ingredients into a bowl and using a spoon mix to combine. Spread over each cake.