Heat the oven to 180ºC/ 350ºF/ gas 4.
Place the sugar, oil and eggs in a bowl and mix together lightly. Stir in the carrots, raisins and hazelnuts. Mix together the flour, oats, bicarbonate of soda and spices. Add to the bowl, mixing lightly until evenly blended. Turn into a greased and base-lined 20cm/ 8 inch square tin, or you can bake it in a round tin or loaf tin if you prefer. Bake for 35-40 minutes until firm to the touch. Turn out and cool on a wire rack.
Beat together the frosting ingredients and spread over the top of the cake.