Peel the carrots and the ginger and then grate them.
Combine the cake flour, whole wheat flour, baking powder, and salt in a bowl and mix together with a whisk.
Gently toast the walnuts in a frying pan. Then put them in a plastic bag and then break them up by crushing them with a rolling pin.
Add the grated carrot, ginger and wet ingredients to the mixture from Step 2. Mix together with a spatula, and then add in the walnuts mixing until the mixture is no longer floury.
Line a cake tin with parchment paper and pour the batter from Step 4 into it. Then gently even it out with a spatula.
Place the cake tin on a baking tray, and bake for 50-60 minutes in an oven preheated to 180. Once baked, remove from the tin and leave the cake to cool.