Line a 20 x 10 cm loaf tin with baking paper.
Preheat the oven to 180°C.
In a medium bowl, mix the dry ingredients (except for the sugar): flours, baking soda, baking powder, cinnamon, and nutmeg.
Using a stand mixer (or hand mixer), beat the whole eggs until fluffy (about 6-8 min). Continue mixing and add the sugar, spoon at the time (about 2 min). Continue mixing and very slowly pour the oil into your batter. Reduce the speed to low, add the dry ingredients, mix until combined.
Add the finely chopped walnuts and grated carrots to the batter and mix everything using a spatula until combined.
Pour the batter into the tin. Bake for about 40 minutes, or until a skewer inserted into the center comes out clean.
To make the frosting, mix the cream cheese with the maple syrup. Spread it over the cooled cake and top with a handful of chopped walnuts (optional). Enjoy!