Preheat your oven to 350°F (175°C). Prepare a 9-inch round cake pan by lightly greasing it or lining it with parchment paper.
Start by grating carrots and chopping walnuts.
In a large bowl, whisk together the flour, granulated sugar, baking powder, cinnamon, ground cloves, ginger, and salt. Fold in raisins and chopped walnuts. Set aside.
In another bowl, combine the oil, applesauce, eggs, brown sugar, and a splash of vanilla extract until well mixed.
Poor wet mixture to the dry ingredients, stirring gently until just combined. Do not overmix! Fold in grated carrots.
Pour the batter into the prepared cake pan and spread it evenly. Bake in the preheated oven for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Once done, remove the cake from the oven, let it cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.
Once your carrot cake is cool, top with a dollop of vanilla yogurt and a sprinkle of chopped walnuts on top for added crunch and flavor.