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1
Heat the oven to 350F (176C). Grease and flour two 9-inch cake pans, and then set them aside. Move the walnuts to a parchment paper-lined baking sheet; when the oven is hot, toast the walnuts for 8 to 10 minutes, or until they smell divine. Remove the walnuts from the oven, and allow them to cool. (When cool, roughly chop the nuts, reserving a couple of whole ones, to garnish the cake with, if you like.)
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2
Meanwhile, peel the carrots and trim the ends off. Grate the carrots. (I use the shredding disk on my food processor, although you can use a box grater, too.) Peel the ginger (use a spoon-it's easier than a vegetable peeler), and then grate the ginger using a microplane, or the smallest holes of a box grater. In a small bowl, stir the ginger into the carrots. Set the bowl aside.
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3
In a large bowl, beat together the eggs and the sugar for 1 to 2 minutes using an electric mixer on medium speed. Add the vanilla. In a separate medium bowl, whisk together the flour, the baking soda, the baking powder, the kosher salt, the cinnamon, and the nutmeg. Fold the dry ingredients into the wet, alternatively adding the melted coconut oil and the yogurt as you go. Zest both the lemon and the orange directly into the mixing bowl. Add the chopped walnuts, the raisins, and the carrots/ginger; fold to incorporate.
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4
Divide the batter between the two pans. Bake for 35-40 minutes, or until a knife comes out clean. Remove the cakes from the oven, and allow them to cool completely. When the cake has cooled, you may slice each round crosswise into two halves, forming four thin cake layers. Or, keep them as they are, for a two layer cake. Frost however you like-the recipe below yields enough frosting to cover four layers, as well as the outside of the cake.
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5
Bring a pot of water to a simmer over medium heat. Meanwhile, add the egg whites, the sugar, and the salt to a metal (read: heatproof) bowl and set it over the warm water-you are creating a water bath, or bain-marie. Whisk the egg whites together with the sugar for 2 to 3 minutes without pause, until the whites heat up and look silky smooth. Rub a bit between two fingers to check that it is no longer grainy-you want the sugar to have dissolved completely into the whites. Carefully take the bowl off the heat.
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6
Using the whisk attachment of an electric mixer on high speed, continue beating the whites until they form firm and lacquered peaks. The whole shebang takes about 10 minutes. Use this time to sing loudly to a couple of your favorite songs. Cut the butter into pieces, and then add it bit by small bit to the whites, continuing to beat on medium speed as you go. Incorporate each piece of butter before you add some more. Remember: just keep beating, just keep beating. Even if it seems like the butter is separating and that all is wrong with the world, I promise that if you keep at it, the frosting will come together. Like the previous step, the butter incorporation takes time to accomplish, so I advise you to continue singing loudly and joyously.
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7
When all the butter has been worked into the whites, add the vanilla and the lemon juice and mix. Add the cream cheese little by little, just like the butter, and then repeat this process with the mascarpone. Again, don't be deterred if the whole thing starts to separate on you. You are strong. You will get through this. (But things will get easier once you add the cream cheese.) Mix until you have a cohesive, light and fluffy frosting, about 10 minutes.
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8
If the cakes are cooled by now, you are ready to start frosting. Feel free to get fancy with a piping bag. If you find the frosting too soft, firm it in the refrigerator for about 20 minutes. This frosting can be made up to 3 days in advance; remove it 20 to 30 minutes before use, to allow it to soften.
