Preheat the oven to 335 degrees fahrenheit. Grease and flour two 6" (3" tall) round cake pans. (*see notes)
In a medium bowl, whisk together the dry ingredients: flour, baking powder, baking soda, cinnamon, ginger, nutmeg, and salt.
In a large bowl, whisk the yolks of the 2 eggs with the white and brown sugars. It will be crumbly and dry in texture. (Be sure to save the egg whites as we will need them later!)Add the liquid fats, oil and melted butter, and whisk until combined. Add the sour cream and whisk until combined. It should be basically the texture of a cake batter at this point. In a measuring cup, stir together the milk, water and vanilla extract.
In a small bowl, whip the 2 egg whites to stiff peaks using an electric mixer. Keep mixing until it is completely white and fluffy, with streaks forming as you mix and so that there is a peak of white that stands straight with only a little curl at the end of the beater when you lift it out of the bowl.
Alternate adding the dry ingredients and the wet ingredients to the bowl of egg yolks, fats and sugar. Begin by pouring in half of the flour mixture and whisking until combined. Then pour in all of the milk mixture and whisk. Finally, pour in the remainder of the flour and whisk.
Fold in the grated carrot and chopped walnuts.
Lightly fold in the whipped egg whites, careful not to completely deflate them. It's okay if there are tiny streaks of egg whites left in the batter.
Divide the batter evenly in the two pans, and bake at 335 for about 60 minutes, or until a toothpick inserted in the centre comes out clean. (see notes*)
Allow the cakes to cool in the pan for about 10 minutes, then flip onto a wire rack and allow to cool completely before frosting.
Enjoy!