Preheat the oven to 180°C (160°C fan). Grease and line a 20–22cm (8–9in) round cake tin with baking paper.
In a large bowl, whisk the eggs and caster sugar for 3–4 minutes, until pale and fluffy.
Gradually add the sunflower oil, whisking continuously until fully combined.
In a separate bowl, sift together the plain flour, baking powder, ground cinnamon, nutmeg (if using) and a pinch of salt.
Fold the dry ingredients into the egg mixture in 2-3 batches, using a spatula, until just combined—avoid overmixing.
Stir in the grated carrots until evenly distributed.
Pour the batter into the prepared tin and bake for 40–45 minutes, or until a skewer inserted into the centre comes out clean.
Allow the cake to cool in the tin for 10 minutes, then turn it out onto a wire rack to cool completely.
For the frosting, beat the softened butter and icing sugar together until smooth.
Add the cold cream cheese and beat on low speed until just combined.
Spread the cream cheese frosting over the cooled cake and, if you like, sprinkle with a little cinnamon or chopped walnuts.