1. Preheat your oven to 180°C (350°F), or 160°C (330°F) if your oven runs hot. Grease and line three 6-inch round cake tins with parchment paper.
2. In a large mixing bowl, sift together the plain flour, caster sugar, light brown sugar, baking soda, baking powder, salt, nutmeg, and cinnamon. Whisk until well combined.
3. In another bowl, beat the eggs, then add the vanilla extract and vegetable oil. Mix well until fully combined.
4. Pour the wet ingredients into the dry ingredients. Mix gently until just combined; do not overmix.
5. Fold in the grated carrots and chopped walnuts or pecans (if using) until evenly distributed.
6. Divide the batter evenly among the three prepared cake tins. Bake in the preheated oven for 20-25 minutes, or until a skewer inserted into the center comes out clean.
7. Once baked, remove the cakes from the oven and allow them to cool in the tins for 10 minutes. Then, carefully turn them out onto wire racks to cool completely.

Cream cheese frosting

1. While the cakes are cooling, prepare the cream cheese frosting. In a mixing bowl, beat the softened butter until creamy. Add the cream cheese and vanilla extract, and continue to beat until smooth. Gradually mix in the icing sugar until fully incorporated.
2. Once the cakes are completely cool, place one layer on a serving plate. Spread a layer of cream cheese frosting over the top. Repeat with the second layer, then place the third layer on top. Frost the top and sides of the cake as desired.
3. Optional: Garnish the top of the cake with additional chopped walnuts or pecans if desired.
4. Slice and serve your delicious carrot cake!