To make the sponge, add the eggs, sugars and oil to a bowl and whisk well until you get a smooth, thick consistency.
Add the grated carrots, sifted flour, spices, vanilla extract and chopped walnuts and mix everything well with a spatula.
Preheat the oven to 180 degrees Celsius (350 Fahrenheit).
Oil and flour a round cake tin (mine is 23 cm, 9 inches), and add the batter to it.
Bake for 45-50 minutes until the sponge is firm to touch and well risen with a golden brown colour and a skewer inserted in the middle comes out clean.
Remove from the tin and allow it to cool.
Use a sharp knife to cut the sponge horizontally into 2 equal-sized sponges.
Meantime, make the icing by adding all the ingredients to a food processor and blitz until smooth.
Alternatively, use a hand mixer to get a smooth icing.
Once the sponges have cooled down, arrange one cake on a plate or cake stand, spread half of the icing over, arrange the second cake on top, and spread the remaining icing over the top and sides.
Decorate with more chopped walnuts.